Answer:
[tex]21\ nickels[/tex]
Step-by-step explanation:
we know that
[tex]1\ nickel= \$0.05[/tex]
[tex]1\ dime= \$0.10[/tex]
Let
x-------> the number of nickels
y-------> the number of dimes
[tex]x+y=37[/tex] ------> isolate the variable y
[tex]y=37-x[/tex] --------> equation A
[tex]0.05x+0.10y=2.65[/tex] ------> multiply by [tex]100[/tex] both sides
[tex]5x+10y=265[/tex] -------> equation B
Substitute equation A in equation B and solve for x
[tex]5x+10(37-x)=265[/tex]
[tex]5x+370-10x=265[/tex]
[tex]10x-5x=370-265[/tex]
[tex]5x=105[/tex]
[tex]x=21\ nickels[/tex]
