Question

aubrey has some pennies and some nickels. she has a maximum of 20 coins worth at least $0.56 combined. aubrey has 5 pennies, determine the minimum number of nickels that she could have.

Explanation:

Step1: Define variables and total coins

Let $n$ = number of nickels. Total coins: $5 + n \leq 20$

Step2: Set up value inequality

Total value: $0.01(5) + 0.05n \geq 0.56$

Step3: Simplify the value inequality

$0.05 + 0.05n \geq 0.56$
Subtract 0.05: $0.05n \geq 0.51$

Step4: Solve for n

$n \geq \frac{0.51}{0.05} = 10.2$
Since $n$ must be integer, $n=11$

Step5: Verify total coins rule

$5 + 11 = 16 \leq 20$, which is valid.

Answer:

11