Question

kat has 19 coins, all quarters and dimes, that are worth a total of $4. the system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
$q + d = 19$
$0.25q + 0.1d = 4$
how many quarters does she have?
○ 4
○ 5
○ 14
○ 15

Explanation:

Step1: Isolate $d$ from first equation

$d = 19 - q$

Step2: Substitute $d$ into second equation

$0.25q + 0.1(19 - q) = 4$

Step3: Expand and simplify the equation

$0.25q + 1.9 - 0.1q = 4$
$0.15q + 1.9 = 4$

Step4: Solve for $q$

$0.15q = 4 - 1.9$
$0.15q = 2.1$
$q = \frac{2.1}{0.15}$

Answer:

14