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Solving Simple Equations - ISEE Lower Level Mathematics Achievement

  1. The sum of a number k and 17 is 43. This is represented by the equation k + 17 = 43. What is the value of k?
    Answer: 26 To find the value of k, you need to isolate it. Subtract 17 from both sides of the equation: k + 17 - 17 = 43 - 17. This simplifies to k = 26.
  2. You buy a snack for xx dollars and add three dollars. If x+3=10x + 3 = 10, what is xx?
    Answer: seven This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario 'x + 3 = 10', x represents the unknown cost of the snack before adding three dollars, and solving it involves subtracting 3 from both sides. Choice A is correct because it correctly identifies x as 7 when you isolate the variable by subtracting 3 from 10 (10 - 3 = 7). Choice B (ten) incorrectly uses the total amount, Choice C (thirteen) results from adding 3 to 10, and Choice D (three) simply repeats the known value. To help students: Create a visual representation showing x dollars plus 3 more dollars equals 10 total. Emphasize checking the answer: 7 + 3 = 10 ✓.
  3. You have twenty stickers, and five are left after giving away xx. For 20−x=520 - x = 5, find xx.
    Answer: fifteen This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '20 - x = 5', x represents the unknown number of stickers given away, and solving it involves finding what number subtracted from 20 equals 5. Choice B is correct because when we solve 20 - x = 5, we get x = 20 - 5 = 15. Choice A (five) incorrectly uses the number of stickers left, Choice C (twenty) uses the starting amount, and Choice D (twenty-five) results from incorrectly adding 20 + 5. To help students: Use physical stickers to demonstrate starting with 20, giving away some, and having 5 left. Verify by substitution: 20 - 15 = 5 ✓.
  4. A recipe calls for a certain amount of flour, f. Sarah doubles the amount and then removes 1 cup. She ends up with 5 cups of flour. This is represented by the equation 2f - 1 = 5. How many cups of flour, f, did the original recipe call for?
    Answer: 3 cups This problem tests your ability to solve linear equations by working backwards from a word problem. When you see a recipe or cooking scenario with mathematical operations, translate each step into algebraic expressions. Let's solve the equation 2f−1=52f - 1 = 5 step by step. To isolate ff, first add 1 to both sides: 2f−1+1=5+12f - 1 + 1 = 5 + 1, which gives us 2f=62f = 6. Then divide both sides by 2: f=3f = 3. We can verify this works: if the original recipe called for 3 cups, Sarah doubled it (3×2=63 \times 2 = 6), then removed 1 cup (6−1=56 - 1 = 5), ending with 5 cups as stated. Choice A (2 cups) represents solving incorrectly by subtracting 1 from 5 instead of adding: 2f=5−1=42f = 5 - 1 = 4, then f=2f = 2. Choice B (6 cups) comes from forgetting to divide by 2 after getting 2f=62f = 6. Choice C (4 cups) might result from adding 1 to the original 3 instead of following the proper algebraic steps, or from misreading the problem setup. The correct answer is D (3 cups). Remember this strategy: when solving equations, always perform the inverse operations in reverse order of how they appear in the problem. Sarah doubled first, then subtracted 1, so you add 1 first, then divide by 2. Always check your answer by substituting back into the original equation.
  5. Mr. Davis started with 30 pencils. After he gave some away, he had 12 left. The equation 30 - p = 12 can be used to find the number of pencils, p, he gave away. What is the value of p?
    Answer: 18 To solve for p in 30 - p = 12, you need to find what number subtracted from 30 equals 12. You can rearrange the equation to 30 - 12 = p. Performing the subtraction, 30 - 12 = 18. So, p = 18.
  6. You need 99 cups of flour. You already have 44 cups. Solve for xx: x+4=9x + 4 = 9.
    Answer: 5 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario needing 9 cups of flour with 4 already, solving x + 4 = 9 involves subtracting 4 from both sides. Choice A is correct because it correctly identifies x as 5 when you isolate the variable by subtracting 4 from 9. Choice B is incorrect because it represents the total without solving. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  7. I am thinking of a number, x. If I divide it by 3 and then add 5, I get 11. The equation is x/3 + 5 = 11. What is the number?
    Answer: 18 To solve x/3 + 5 = 11, first subtract 5 from both sides: x/3 = 11 - 5, which gives x/3 = 6. To find x, multiply both sides by 3: x = 6 × 3, which means x = 18.
  8. A bus has n seats. A group of passengers fills half the seats. Then, 3 more passengers get on. Now, there are 26 passengers on the bus. The equation n/2 + 3 = 26 represents this situation. What is the total number of seats, n, on the bus?
    Answer: 46 To solve the equation n/2 + 3 = 26, first subtract 3 from both sides: n/2 = 26 - 3, which simplifies to n/2 = 23. This means that half the number of seats is 23. To find the total number of seats, n, multiply 23 by 2: n = 23 × 2 = 46. The bus has 46 seats.
  9. Tia wants 2020 dollars saved. She needs 55 more. If 20−x=520 - x = 5, find xx.
    Answer: 15 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where Tia wants $20 and needs $5 more, solving 20 - x = 5 gives x as saved amount of 15. Choice B is correct because it correctly identifies x as 15 when you isolate the variable. Choice A is incorrect because it uses the needed amount directly. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  10. You bike five miles and then xx miles. If 5+x=155 + x = 15, what is xx?
    Answer: ten This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '5 + x = 15', x represents the unknown number of miles biked after the first five miles, and solving it involves subtracting 5 from both sides. Choice B is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15 (15 - 5 = 10). Choice A (twenty) results from adding 5 to 15, Choice C (fifteen) incorrectly uses the total distance, and Choice D (five) simply repeats the known value. To help students: Use visual aids like number lines to show how subtraction helps find the missing part. Practice with real-world contexts to make the concept more concrete and relatable.
  11. A baker uses 99 cups of flour. Four cups are already in the bowl. If x+4=9x + 4 = 9, find xx.
    Answer: 5 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where a baker uses 9 cups with 4 already in the bowl, solving x + 4 = 9 involves subtracting 4 from both sides. Choice C is correct because it correctly identifies x as 5 when you isolate the variable by subtracting 4 from 9. Choice A is incorrect because it uses the added amount directly. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  12. A rectangular garden has a length of 10 feet and a perimeter of 34 feet. The formula for the perimeter is P = 2l + 2w. For this garden, the equation is 34 = 2(10) + 2w. What is the width, w, of the garden?
    Answer: 7 feet Start with the equation 34 = 2(10) + 2w. First, calculate 2(10), which is 20. The equation becomes 34 = 20 + 2w. Next, subtract 20 from both sides: 34 - 20 = 2w, which simplifies to 14 = 2w. Finally, divide by 2 to find w: 14 / 2 = 7. The width is 7 feet.
  13. The equation (□ × 6) + 5 = 29 is true. What number belongs in the box?
    Answer: 4 Let the number in the box be n. The equation is 6n + 5 = 29. First, subtract 5 from both sides: 6n = 29 - 5, so 6n = 24. Then, divide both sides by 6: n = 24 / 6, which gives n = 4. The number 4 belongs in the box.
  14. Mia has ten dollars. She buys a snack for 33. Solve for xx: x+3=10x + 3 = 10. What is xx?
    Answer: 7 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario where Mia has ten dollars and buys a snack for $3, x represents the money left, and solving x + 3 = 10 involves subtracting 3 from both sides. Choice B is correct because it correctly identifies x as 7 when you isolate the variable by subtracting 3 from 10. Choice A is incorrect because it results from misunderstanding the equation as subtraction without isolation. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  15. A trail is 1515 miles. Pat walks 55 miles. For 5+x=155 + x = 15, find xx.
    Answer: 10 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario of a 15-mile trail where Pat walks 5 miles, solving 5 + x = 15 involves subtracting 5 from both sides. Choice A is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15. Choice B is incorrect because it might result from subtracting incorrectly. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  16. A group of friends shared a bag of 48 candies equally. After sharing, each friend had 6 candies. The equation 48 / n = 6 represents this situation, where n is the number of friends. How many friends were in the group?
    Answer: 8 To solve for n, you can rewrite the division equation as a multiplication equation: 6 × n = 48. Then, divide 48 by 6 to find n: n = 48 / 6 = 8. There were 8 friends in the group.
  17. A walk is 1515 miles total. Jay finishes 55 miles. Solve 5+x=155 + x = 15 for xx.
    Answer: 10 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario of a 15-mile walk where Jay finishes 5 miles, solving 5 + x = 15 involves subtracting 5 from both sides. Choice B is correct because it correctly identifies x as 10 when you isolate the variable by subtracting 5 from 15. Choice A is incorrect because it mistakes the remaining for the walked. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  18. You have ten dollars total and spend three dollars. Solve for xx: 3+x=103 + x = 10.
    Answer: seven This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '3 + x = 10', x represents the unknown amount of money remaining after spending three dollars from a ten-dollar total, and solving it involves subtracting 3 from both sides. Choice A is correct because it correctly identifies x as 7 when you isolate the variable by subtracting 3 from 10 (10 - 3 = 7). Choice B (ten) incorrectly uses the total amount, Choice C (thirteen) results from adding 3 to 10, and Choice D (three) repeats the amount spent. To help students: Use play money to show spending $3 from $10 and finding what's left. Practice writing equations from word problems to strengthen the connection.
  19. A recipe needs 99 cups of flour total. You add 44 cups. If x+4=9x + 4 = 9, what is xx?
    Answer: 5 This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario of a recipe needing 9 cups of flour with 4 added, x is additional needed, and solving x + 4 = 9 involves subtracting 4 from both sides. Choice B is correct because it correctly identifies x as 5 when you isolate the variable by subtracting 4 from 9. Choice A is incorrect because it adds instead of subtracting. To help students: Teach strategies like balancing equations by performing the same operation on both sides. Encourage checking work by substituting values back into the original equation.
  20. In a store, you spend three dollars and xx dollars. If 3+x=103 + x = 10, what is xx?
    Answer: seven This question tests solving for an unknown in a simple equation (ISEE Lower Level Mathematics Achievement). Understanding simple equations involves isolating the variable to find its value. In the scenario '3 + x = 10', x represents the unknown amount of dollars spent in addition to three dollars, and solving it involves subtracting 3 from both sides. Choice B is correct because it correctly identifies x as 7 when you isolate the variable by subtracting 3 from 10 (10 - 3 = 7). Choice A (three) is incorrect because it simply repeats the known value, Choice C (ten) incorrectly uses the total, and Choice D (thirteen) results from adding instead of subtracting. To help students: Teach the concept of inverse operations - if the equation uses addition, use subtraction to solve. Encourage students to check their answer by substituting it back: 3 + 7 = 10 ✓.

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