ISEE Lower Level Mathematics Achievement Quiz: Equation From A Situation

What this quiz covers

This quiz focuses on Equation From A Situation, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. (a + b = 10)
2. (75a + 50b = 10)
3. (0.75a + 0.50b = 10) (correct answer)
4. (0.50a + 0.75b = 10)

Explanation: The total cost of the apples is the price per apple (0.75) times the number of apples (*a*), which is \(0.75a\). The total cost of the bananas is the price per banana (0.50) times the number of bananas (b), which is (0.50b). The sum of these costs is equal to the total amount spent, $10. So, the equation is (0.75a + 0.50b = 10).

Question 2

1. (b = 2r)
2. (r = b + 2)
3. (r = 2b) (correct answer)
4. (b = r - 2)

Explanation: The statement 'the number of red marbles, r, is exactly double the number of blue marbles, b' means you must multiply the number of blue marbles by 2 to get the number of red marbles. This translates to the equation (r = 2b).

Question 3

1. (p = 350d - 25)
2. (p = 25d)
3. (p = 350 - 25d) (correct answer)
4. (d = 350 - 25p)

Explanation: The total number of pages is 350. The number of pages read after d days is (25d). The number of pages left, p, is the total number of pages minus the number of pages read. This gives the equation (p = 350 - 25d).

Question 4

1. (F = \frac{9}{5}C + 32) (correct answer)
2. (F = \frac{9}{5}(C + 32))
3. (F = 9(\frac{C}{5} + 32))
4. (C = \frac{9}{5}F + 32)

Explanation: Following the steps in order: 'multiplying the temperature in degrees Celsius, C, by 9' gives (9C). 'dividing the result by 5' gives (\frac{9C}{5}). 'then adding 32' gives (\frac{9C}{5} + 32). This is the value of F. The expression (\frac{9C}{5}) is the same as (\frac{9}{5}C), so the equation is (F = \frac{9}{5}C + 32).

Question 5

1. (A = 50 - 15w)
2. (A = 15 + 50w)
3. (A = 50 + 15w) (correct answer)
4. (w = 50 + 15A)

Explanation: The total amount A starts at $50 and increases over time. The amount added is$15 per week, which is (15w). Therefore, the total amount is the starting amount plus the added amount: (A = 50 + 15w).

Question 6

1. (C = (20 + 15)p) (correct answer)
2. (C = 20p + 15)
3. (C = 20 + 15p)
4. (C = p + 20 + 15)

Explanation: First, find the cost for one player. One player needs one jersey ($20) and one pair of shorts ($15), for a total of ($20 +$15 = $35). To find the total cost C for p players, multiply the cost per player by the number of players. This gives the equation (C = 35p), which is the same as (C = (20 + 15)p).

Question 7

1. (a + c = 950)
2. (11a + 8c = 950) (correct answer)
3. (8a + 11c = 950)
4. (19(a + c) = 950)

Explanation: The total money from adult tickets is the price per ticket (11) times the number of tickets (*a*), which is \(11a\). The total money from child tickets is the price per ticket (8) times the number of tickets (c), which is (8c). The total money collected is the sum of these two amounts, so (11a + 8c = 950).

Question 8

1. (C = 25 + 0.10t)
2. (C = 25 + 0.10(t - 500)) (correct answer)
3. (C = 25.10(t - 500))
4. (C = 25 + 0.10(500 - t))

Explanation: The base cost is $25. The extra charge only applies to texts over 500. The number of texts that are charged extra is (t - 500). The cost for these extra texts is (0.10(t - 500)). The total cost C is the base cost plus the extra charge: (C = 25 + 0.10(t - 500)).

Question 9

1. (F = 50 + 3c)
2. (F = 3c - 50)
3. (c = 50 - 3F)
4. (F = 50 - 3c) (correct answer)

Explanation: The initial amount of flour is 50 pounds. The amount used is 3 pounds per cake, so for c cakes, the amount used is (3c). The remaining flour, F, is the starting amount minus the amount used. This gives the equation (F = 50 - 3c).

Question 10

1. (F = 12 - s)
2. (F = \frac{s}{12})
3. (F = \frac{12 - s}{12}) (correct answer)
4. (F = \frac{12}{s})

Explanation: First, find the number of slices remaining. If the pizza starts with 12 slices and s slices are eaten, there are (12 - s) slices left. The fraction of the pizza remaining is the number of remaining slices divided by the original total number of slices. Therefore, the fraction F is (\frac{12 - s}{12}).

Question 11

1. (G = 15h - 2)
2. (G = 15 - 2h) (correct answer)
3. (G = 2h - 15)
4. (h = 15 - 2G)

Explanation: The starting amount of gas is 15 gallons. Gas is used, so the amount will decrease. The amount used is 2 gallons per hour, or (2h) for h hours. The remaining gas, G, is the initial amount minus the amount used, which is represented by the equation (G = 15 - 2h).

Question 12

1. (f = 3n - 150) (correct answer)
2. (n = 3f - 150)
3. (f = 3(n - 150))
4. (f = 150 - 3n)

Explanation: The phrase 'three times the number of non-fiction books' translates to (3n). The phrase '150 fewer than' means we subtract 150 from that amount. Therefore, the number of fiction books, f, is equal to (3n - 150).

Question 13

1. (P = w(w + 4))
2. (P = w + (w+4))
3. (P = 2w + 4)
4. (P = 2w + 2(w + 4)) (correct answer)

Explanation: The perimeter of a rectangle is found with the formula (P = 2l + 2w), where l is the length and w is the width. The problem states the length is '4 inches longer than its width, w', so (l = w + 4). Substituting this into the perimeter formula gives (P = 2(w + 4) + 2w), which can be written as (P = 2w + 2(w + 4)).

Question 14

1. (l = k - 5)
2. (k + l = 5)
3. (k = l + 5)
4. (k = l - 5) (correct answer)

Explanation: The statement 'Ken is 5 inches shorter than Leo' means that to find Ken's height, k, you must subtract 5 inches from Leo's height, l. This relationship is written as the equation (k = l - 5).

Question 15

1. (F = s^2 - 3)
2. (F = 4s - 3) (correct answer)
3. (F = 4(s - 3))
4. (F = 4s + 3)

Explanation: The perimeter of a square is 4 times the side length, so the total perimeter is (4s). Since a 3-foot section is left open, the length of the fencing, F, is the perimeter minus the length of the gate. This is represented by the equation (F = 4s - 3).

Question 16

1. (d = 2s - 7) (correct answer)
2. (s = 2d - 7)
3. (d = 2(s - 7))
4. (d = 7 - 2s)

Explanation: The phrase 'twice his sister Sarah's age, s' translates to (2s). The phrase '7 years less than' means you subtract 7 from that amount. Therefore, David's age, d, is represented by the equation (d = 2s - 7).

Question 17

1. (S = 4c + b)
2. (S = c - 4b)
3. (S = 4(c - b))
4. (S = 4c - b) (correct answer)

Explanation: Points are earned for correct answers and deducted for blank answers. The points earned are (4c). The points deducted are (1b), or simply b. The total score S is the points earned minus the points deducted, so (S = 4c - b).

Question 18

1. (S = 5c + 2t)
2. (S = 5c - 2t) (correct answer)
3. (S = 2c - 5t)
4. (S = c + t - 7)

Explanation: The points from coins are calculated by multiplying the number of coins, c, by 5 ((5c)). The points lost from traps are calculated by multiplying the number of traps, t, by 2 ((2t)). Since points are lost for traps, this amount is subtracted from the points gained. The total score S is (5c - 2t).

Question 19

1. (q + d = 42)
2. (V = 0.25q + 0.10d)
3. (V = 25q + 10d) (correct answer)
4. (V = q + d)

Explanation: The question asks for the total value in cents. A quarter is worth 25 cents and a dime is worth 10 cents. The value of the quarters is (25q) and the value of the dimes is (10d). The total value V is the sum of these values: (V = 25q + 10d). The information about 42 total coins is extra and does not relate to the value.

Question 20

1. (C = 12g + 100) (correct answer)
2. (C = 100g + 12)
3. (C = (100 + 12)g)
4. (g = 100 + 12C)

Explanation: The total cost C is the sum of the fixed fee ($100) and the variable cost, which depends on the number of guests. The variable cost is$12 multiplied by the number of guests, g, or (12g). So, the total cost is (C = 100 + 12g), which is the same as (C = 12g + 100).