Question

You have total coins for a total of $. . You only have quarters and dimes. Let represent the number of quarters and represent the number of dimes.

Answer 1

Answer:

$Quarters = 41$

$Dimes = 18$

Step-by-step explanation:

Given

$Coins = 59$

$Worth = \ 12.05$

$d = dimes$

$q = quarters$

Required

The number of each coin

The total coins can be represented as:

$d + q = 59$

$1\ quarter = \ 0.25 \\ 1\ dime = \ 0.10$

So, the worth of the coin is:

$0.25q + 0.10d = 12.05$

The equations to solve are:

$0.25q + 0.10d = 12.05$

$d + q = 59$

Make d the subject in: $d + q = 59$

$d =59 - q$

Substitute $d =59 - q$ in $0.25q + 0.10d = 12.05$

$0.25q + 0.10(59 - q) = 12.05$

$0.25q + 5.9 - 0.10q = 12.05$

Collect like terms

$0.25q - 0.10q = 12.05 - 5.9$

$0.15q = 6.15$

Solve for q

$q=\frac{6.15}{0.15}$

$q=41$

Substitute $q=41$ in $d =59 - q$

$d = 59 - 41$

$d = 18$

So:

$Quarters = 41$

$Dimes = 18$