Question

write and solve a system of equations. show work on your recording sheet. enter answer here. dustin has only nickels and quarters in his piggy bank. he has 49 coins total for a combined value of $8.85. how many of each type of coin does he have? dustin has 14 nickels and 35 quarters in his piggy bank.

Explanation:

Step1: Define variables

Let $n$ = number of nickels, $q$ = number of quarters.

Step2: Total coins equation

Total coins: $n + q = 49$

Step3: Total value equation

Value in dollars: $0.05n + 0.25q = 8.85$

Step4: Isolate $n$ from Step2

$n = 49 - q$

Step5: Substitute into value equation

$0.05(49 - q) + 0.25q = 8.85$
$2.45 - 0.05q + 0.25q = 8.85$
$2.45 + 0.20q = 8.85$

Step6: Solve for $q$

$0.20q = 8.85 - 2.45$
$0.20q = 6.40$
$q = \frac{6.40}{0.20} = 32$

Step7: Solve for $n$

$n = 49 - 32 = 17$

Answer:

Dustin has $\boldsymbol{17}$ nickels and $\boldsymbol{32}$ quarters in his piggy bank.