Solving for an Unknown
Help Questions
ISEE Middle Level: Mathematics Achievement › Solving for an Unknown
A streaming service charges $12 each month plus a $5 one-time fee. After a few months, the total cost is $53. Let $x$ be the number of months paid for. This situation is represented by $12x + 5 = 53$. If $12x + 5 = 53$, what is $x$?
$x = 48$
$x = 58$
$x = 4$
$x = 5$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 12x + 5 = 53, where the unknown variable is isolated by subtracting 5 from both sides to get 12x = 48 and then dividing by 12 to find x = 4. The correct answer, choice A, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice B is incorrect due to a common arithmetic error where students forget to subtract and divide 53 by something to get x = 48. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
Maya buys 3 notebooks and 1 binder, and the total is $18. The binder costs $6. The notebooks all cost the same amount, and sales tax is already included. The situation can be modeled by $3x + 6 = 18$, where $x$ is the price of one notebook. If $3x + 6 = 18$, what is $x$?
$x = 4$
$x = 12$
$x = 8$
$x = 6$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 3x + 6 = 18, where the unknown variable is isolated by subtracting 6 from both sides to get 3x = 12 and then dividing by 3 to find x = 4. The correct answer, choice B, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice A is incorrect due to a common arithmetic error where students add 6 instead of subtracting, leading to 3x = 24 and x = 8. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A bus travels 150 miles in 3 hours at a constant speed. The driver keeps the same speed for the whole trip. Let $x$ be the speed in miles per hour. The situation can be written as $3x = 150$. If $3x = 150$, what is $x$?
$x = 47$
$x = 53$
$x = 50$
$x = 450$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 3x = 150, where the unknown variable is isolated by dividing both sides by 3 to find x = 50. The correct answer, choice C, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice A is incorrect due to a common arithmetic error where students multiply instead of dividing, such as 3 * 150 = 450. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A baker makes 5 identical loaves and sells them for $40 total. Each loaf has the same price, and there are no coupons. Let $x$ be the price of one loaf. The situation is represented by $5x = 40$. Determine the value of $x$ when $5x = 40$.
$x = 10$
$x = 8$
$x = 200$
$x = 35$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 5x = 40, where the unknown variable is isolated by dividing both sides by 5 to find x = 8. The correct answer, choice A, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice B is incorrect due to a common arithmetic error where students multiply instead of dividing, such as 5 * 40 = 200. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A recipe uses 2 cups of flour for 8 muffins. Sam wants to make 24 muffins and keeps the same recipe ratio. Let $x$ be the number of cups of flour needed. The situation can be written as $8x = 48$. Solve for $x$ in the equation $8x = 48$.
$x = 6$
$x = 5$
$x = 40$
$x = 8$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 8x = 48, where the unknown variable is isolated by dividing both sides by 8 to find x = 6. The correct answer, choice A, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice B is incorrect due to a common arithmetic error where students multiply instead of dividing, such as 8 * 5 = 40. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A runner completes 24 miles over 4 days, running the same distance each day. No rest days are included in the total. Let $x$ be the miles run each day. The situation is modeled by $4x = 24$. If $4x = 24$, what is $x$?
$x = 20$
$x = 8$
$x = 28$
$x = 6$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 4x = 24, where the unknown variable is isolated by dividing both sides by 4 to find x = 6. The correct answer, choice B, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice A is incorrect due to a common arithmetic error where students multiply instead of dividing, such as 4 * 7 = 28. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A class orders 9 identical pizzas for a total of $99. Each pizza costs the same amount, and delivery is free. Let $x$ be the cost of one pizza. The situation is represented by $9x = 99$. Solve for $x$ in the equation $9x = 99$.
$x = 110$
$x = 90$
$x = 11$
$x = 9$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 9x = 99, where the unknown variable is isolated by dividing both sides by 9 to find x = 11. The correct answer, choice C, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice A is incorrect due to a common arithmetic error where students divide incorrectly, such as 99 / 11 = 9. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A car travels at a constant speed for 3 hours and goes 180 miles. The driver does not stop, and the distance stays the same the whole time. Let $x$ be the car’s speed in miles per hour. The situation can be written as $3x = 180$. Solve for $x$ in the equation $3x = 180$.
$x = 63$
$x = 540$
$x = 60$
$x = 30$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 3x = 180, where the unknown variable is isolated by dividing both sides by 3 to find x = 60. The correct answer, choice A, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice B is incorrect due to a common arithmetic error where students multiply instead of dividing, such as 3 * 180 = 540. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A taxi charges a $4 start fee plus $2 per mile. Jordan’s ride costs $18 total, including the start fee. Let $x$ be the number of miles traveled. This situation is represented by $2x + 4 = 18$. If $2x + 4 = 18$, what is $x$?
$x = 11$
$x = 9$
$x = 14$
$x = 7$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 2x + 4 = 18, where the unknown variable is isolated by subtracting 4 from both sides to get 2x = 14 and then dividing by 2 to find x = 7. The correct answer, choice C, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice A is incorrect due to a common arithmetic error where students subtract incorrectly, such as 18 - 4 = 14 but then divide by something else leading to x = 11. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.
A bookstore sells a novel for $x dollars, and a bookmark costs $2. Ava buys 4 novels and 1 bookmark for $34 total. All novels have the same price. The situation is modeled by $4x + 2 = 34$. Find $x$ if $4x + 2 = 34$.
$x = 32$
$x = 9$
$x = 8$
$x = 7$
Explanation
This question tests middle school mathematics skills: solving linear equations for an unknown variable. To solve for an unknown, isolate the variable by performing inverse operations—undo addition with subtraction, multiplication with division, etc. In this scenario, the equation presented is 4x + 2 = 34, where the unknown variable is isolated by subtracting 2 from both sides to get 4x = 32 and then dividing by 4 to find x = 8. The correct answer, choice B, reflects the accurate isolation and calculation of the variable, ensuring the equation balances. Choice C is incorrect due to a common arithmetic error where students forget to subtract and divide 34 by something to get x = 32. To help students master this skill, practice breaking down equations step-by-step, checking each inverse operation. Encourage identifying operations by highlighting terms that need isolation and using manipulatives or visual aids to reinforce understanding.