Answer:
Nickel = 12
Quarters = 26
Step-by-step explanation:
Given
Represent Nickel with N and Quarters with Q
[tex]Q = 14 + N[/tex] --- It's 14 more quarters; not 143
[tex]Worth = \$7.10[/tex]
Required
Determine the quantity of each coin
First, we have to know that:
[tex]0.25Q + 0.05N = 7.10[/tex] -- (1) ---- By converting N and Q to dollars;
[tex]Q = 14 + N[/tex]
Substitute 14 + N for Q in (1)
[tex]0.25(14 + N) + 0.05N = 7.10[/tex]
Open Brackets
[tex]3.5 + 0.25N + 0.05N = 7.10[/tex]
Collect Like Terms
[tex]0.25N + 0.05N = 7.10 - 3.5[/tex]
[tex]0.3N = 3.6[/tex]
Divide through by 0.3
[tex]N = 3.6/0.3[/tex]
[tex]N = 12[/tex]
Recall that:
[tex]Q = 14 + N[/tex]
[tex]Q = 14 + 12[/tex]
[tex]Q = 26[/tex]
