Exponents
Simplify: 3⁴ + 2³ × 5
121
81 + 40 = 121
A number is 240% of 75. What is the number?
180
75 × 2.4 = 180
A recipe uses 3 cups of flour to make 8 muffins. How many cups of flour are needed to make 28 muffins, assuming the recipe stays proportional?
10.5 cups
7x + 23 = 100
Solve for x
X = 1
(100 - 23) ÷ 7 = 11
Simplify the ratio 84:126.
2:3
84:126 = 2:3
Simplify: 2⁵ × 2³ ÷ 2⁴
24 = 16
A jacket costs $160 after a 20% discount. What was the original price?
$200
160 ÷ 0.8 = $200
A car travels 156 km using 12 L of gasoline. At the same rate, how far can it travel using 17.5 L?
227.5 km
Solve for x:
9x - 34 = 110
x = 16
(110 + 34) ÷ 9 = 16
The ratio of boys to girls in a class is 5:7. If there are 36 students, how many are girls?
21 girls
36 × 7/12 = 21 girls
Simplify: (3²)³ ÷ 3⁴
9
3² = 9
A population of 8,000 increases by 12.5% and then decreases by 8%. What is the final population?
8280
8,000 × 1.125 × 0.92 = 8,280
If Y was directly proportional to X, and Y = 42 when X = 14, what was the value of X when Y = 96.
x = 32
Solve for x:
13x + 47 = 216
x = 13
(216 - 47) ÷ 13 = 13
The ratio of red to blue marbles is 4:9. There are 65 marbles in total. How many more blue marbles are there than red marbles?
25 marbles
65 ÷ 13 = 5, then (9 − 4) × 5 = 25 marbles
Simplify: 5³ - 2⁴ × 3 + 7²
126
125 - 48 + 49 = 126
After increasing by 40%, a number becomes 196. What was the original number?
140
196 ÷ 1.4 = 140
Y is directly proportional to X. When X=8, Y=14. Find Y when X=26.
Y = 45.5
Solve for x:
17x - 68 = 221
x = 17
(221 + 68) ÷ 17 = 17
The ratio of A to B is 3:5, and the ratio of B to C is 10:7. What is the ratio A:B:C in simplest form?
6 : 10 : 7
3:5 = 6:10, so A:B:C = 6:10:7
Simplify: (2³ × 4²) ÷ 2⁵ + 3³
31
8 × 16 ÷ 32 + 27 = 31
A price increases by 25%, then decreases by 20%, and then increases by 10%. If the final price is $330, what was the original price?
$300
330 ÷ (1.25 × 0.8 × 1.1) = $300
A number is increased by 35%, then the new value is decreased by 20%. The final result is 216. What was the original number?
200
23x + 89 = 526
x = 19
(526 - 89) ÷ 23 = 19
The ratio of two numbers is 7:11. If 12 is added to each number, the ratio becomes 5:7. What are the original numbers?
21 and 33
(12 × 2) ÷ (7 − 5) = 12, so the original numbers are 7 × 3 = 21 and 11 × 3 = 33