Let’s solve each problem one by one.
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Problem 1:
Jake buys:
- 3 apples at $0.89 each → cost = 3 × 0.89
- 2 cans of soup at $2.98 each → cost = 2 × 2.98
- 1 box of cereal at $4.99 → cost = 4.99
Total cost c = (3 × 0.89) + (2 × 2.98) + 4.99
Look at the options:
A: adds quantities and prices together — wrong
B: multiplies sums — wrong
C: matches our calculation
✔
D: multiplies all parts — wrong
✔ Correct answer:
C
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Problem 2:
Mr. Thomas makes 48 monthly payments of $161.85 to pay back a loan with interest.
We want to find how much he originally borrowed.
To do that, we need to know how much total he paid (which we can calculate: 48 × 161.85), but that includes interest. To separate principal from interest, we need to know the
interest rate.
Without knowing the interest rate, we can’t figure out how much was borrowed vs. how much is interest.
So, what else is necessary? → The interest rate.
Options:
F: His income — irrelevant
G: Interest rate — YES
✔
H: Boat license — irrelevant
J: Value increase — irrelevant
✔ Correct answer:
G
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Problem 3:
Ricky jogs 5 laps in 8 minutes → rate = 5/8 laps per minute = 0.625 laps/min
Check which option has same rate:
A: 7 / 9.6 ≈ 0.729 → no
B: 10 / 15.6 ≈ 0.641 → no
C: 12 / 19.2 = ? Let’s compute: 12 ÷ 19.2 = 120 ÷ 192 = 5/8 = 0.625 → YES
✔
D: 8 / 20 = 0.4 → no
✔ Correct answer:
C
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Problem 4:
Mercury is 5.80 × 10⁷ km from Sun.
Standard notation means write it as a regular number.
10⁷ = 10,000,000 → so 5.80 × 10,000,000 = 58,000,000
Check options:
F: too small
G: even smaller
H: 5,800,000 → that’s 5.8 × 10⁶ → too small
J: 58,000,000 → correct
✔
✔ Correct answer:
J
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Problem 5:
Expression: 8⁻⁵ × 8²
When multiplying powers with same base, add exponents:
8^(-5 + 2) = 8^(-3)
Negative exponent means reciprocal: 8^(-3) = 1 / 8³
Check options:
A: 1/8⁷ → no
B: 1/8³ → YES
✔
C: 8³ → no
D: 8⁷ → no
✔ Correct answer:
B
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Final Answer:
1. C
2. G
3. C
4. J
5. B
Parent Tip: Review the logic above to help your child master the concept of advanced math worksheet.
