Let’s solve each problem one by one, step by step.
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Problem 1:
A car averages 27 miles per gallon. Gas costs $4.04 per gallon. How much does it cost to travel 2,727 miles?
Step 1: Find how many gallons are needed for 2,727 miles.
Gallons = Total miles ÷ Miles per gallon
→ 2,727 ÷ 27
Let’s calculate that:
27 × 100 = 2,700 → so 2,727 - 2,700 = 27 → that’s exactly 1 more gallon.
So 100 + 1 =
101 gallons
Step 2: Multiply gallons by cost per gallon.
Cost = 101 × $4.04
Break it down:
100 × 4.04 = 404
1 × 4.04 = 4.04
Total = 404 + 4.04 =
$408.04
That matches option D.
✔ Final Answer for Problem 1:
D. $408.04
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Problem 2:
When x = 3 and y = 5, by how much does 3x² – 2y exceed 2x² – 3y?
We need to compute both expressions and subtract the second from the first.
First expression: 3x² – 2y
Plug in x=3, y=5:
3*(3)² – 2*5 = 3*9 – 10 = 27 – 10 =
17
Second expression: 2x² – 3y
2*(3)² – 3*5 = 2*9 – 15 = 18 – 15 =
3
Now find the difference: 17 – 3 =
14
✔ Final Answer for Problem 2:
G. 14
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Problem 3:
Solve for x: 2x + 3 = 3x – 4
Get all x terms on one side, constants on the other.
Subtract 2x from both sides:
3 = x – 4
Add 4 to both sides:
3 + 4 = x →
x = 7
✔ Final Answer for Problem 3:
E. 7
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Problem 4:
Find the greatest common factor (GCF) of 42, 126, and 210.
List factors or use prime factorization.
Prime factorization:
- 42 = 2 × 3 × 7
- 126 = 2 × 3² × 7
- 210 = 2 × 3 × 5 × 7
Common primes: 2, 3, and 7 appear in all three.
Multiply them: 2 × 3 × 7 =
42
Check: Is 42 a factor of all?
42 ÷ 42 = 1
✔
126 ÷ 42 = 3
✔
210 ÷ 42 = 5
✔
Yes! So GCF is 42.
✔ Final Answer for Problem 4:
J. 42
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Problem 5:
Sales:
- Second year = First year + 3 million
- Third year = Double the second year
- Third year sales = 38 million
Let first year = F
Then second year = F + 3
Third year = 2 × (F + 3) = 38
So:
2(F + 3) = 38
Divide both sides by 2:
F + 3 = 19
Subtract 3:
F = 16
✔ Final Answer for Problem 5:
A. 16
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Final Answer:
1. D
2. G
3. E
4. J
5. A
Parent Tip: Review the logic above to help your child master the concept of act math practice worksheet.
