Answer:
[tex]Quarters = 41[/tex]
[tex]Dimes = 18[/tex]
Step-by-step explanation:
Given
[tex]Coins = 59[/tex]
[tex]Worth = \$12.05[/tex]
[tex]d = dimes[/tex]
[tex]q = quarters[/tex]
Required
The number of each coin
The total coins can be represented as:
[tex]d + q = 59[/tex]
[tex]1\ quarter = \$0.25 \\ 1\ dime = \$0.10[/tex]
So, the worth of the coin is:
[tex]0.25q + 0.10d = 12.05[/tex]
The equations to solve are:
[tex]0.25q + 0.10d = 12.05[/tex]
[tex]d + q = 59[/tex]
Make d the subject in: [tex]d + q = 59[/tex]
[tex]d =59 - q[/tex]
Substitute [tex]d =59 - q[/tex] in [tex]0.25q + 0.10d = 12.05[/tex]
[tex]0.25q + 0.10(59 - q) = 12.05[/tex]
[tex]0.25q + 5.9 - 0.10q = 12.05[/tex]
Collect like terms
[tex]0.25q - 0.10q = 12.05 - 5.9[/tex]
[tex]0.15q = 6.15[/tex]
Solve for q
[tex]q=\frac{6.15}{0.15}[/tex]
[tex]q=41[/tex]
Substitute [tex]q=41[/tex] in [tex]d =59 - q[/tex]
[tex]d = 59 - 41[/tex]
[tex]d = 18[/tex]
So:
[tex]Quarters = 41[/tex]
[tex]Dimes = 18[/tex]
