Answer:
14 dimes, 21 quarters
Step-by-step explanation:
Represent dimes with d and quarters with q.
So: 35 coins means
[tex]d + q = 35[/tex]
1 dime = $0.10 and 1 quarter = $0.25. So, a value of $5.60 means
[tex]0.10d + 0.25q = 5.60[/tex]
So, the system of equations is:
[tex]d + q = 35[/tex]
[tex]0.10d + 0.25q = 5.60[/tex]
Make d the subject in [tex]d + q = 35[/tex]
[tex]d = 35 - q[/tex]
Substitute 35 - q for d in [tex]0.10d + 0.25q = 5.60[/tex]
[tex]0.10d + 0.25(35 - q) = 5.60[/tex]
Open bracket
[tex]0.10d + 8.75 - 0.25q = 5.60[/tex]
Collect Like Terms
[tex]0.10d - 0.25q = 5.60 - 8.75[/tex]
[tex]-0.15q = -3.15[/tex]
Solve for q
[tex]q = \frac{-3.15}{-0.15}[/tex]
[tex]q = 21[/tex]
Substitute 21 for q in [tex]d = 35 - q[/tex]
[tex]d = 35 - 21[/tex]
[tex]d = 14[/tex]
