Danny has $\$2.14$ in pennies and nickels in his piggy bank. The number of nickels is **two more than ten times** the number of pennies. How many pennies does Danny have?
A$4$
B$10$
C$14$
D$42$
Answer & Solution
Correct answer: A. $4$
Let $p$ be the number of pennies. Then $10p + 2$ is the number of nickels.
Total value: $0.01 p + 0.05 (10p + 2) = 2.14$.
Distribute: $0.01 p + 0.50 p + 0.10 = 2.14$.
Combine: $0.51 p + 0.10 = 2.14$.
Subtract $0.10$: $0.51 p = 2.04$.
Divide: $p = 4$.
So Danny has $4$ pennies and $10(4) + 2 = 42$ nickels.
Check: $4(0.01) + 42(0.05) = 0.04 + 2.10 = \$2.14$ ✓.
- Trap D ($42$) is the number of **nickels**, not pennies. Read carefully.
- Trap B ($10$) and C ($14$) come from misinterpreting the relationship between counts.
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