Respuesta :
the number of nickles is 38
C: 53
Explanation
Step 1
set the equations
Let x represents the number of dimes
1 dime= 0.10 dollar = $ 0.10
let y represents the number of nickles
1 nickel ? 0.05 dolars = $0.05
so
a)Jonah has collected 91 coins
[tex]x+y=91\Rightarrow equation(1)[/tex]b) it worth $7.20,
hence
[tex]0.1x+0.05y=7.20\Rightarrow equation(2)[/tex]Step 2
solve the eqautions
a) isolate x in equation and replace the result in equation (2)
[tex]\begin{gathered} x+y=91\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=91-y \\ x=91-y \end{gathered}[/tex]replace in equation (2)
[tex]\begin{gathered} 0.1x+0.05y=7.20\Rightarrow equation(2) \\ 0.1(91-y)+0.05y=7.20 \\ 9.1-0.1y+0.05y=7.20 \\ 9.1-0.05y=7.2 \\ \text{subtrac 9.1 in both sides} \\ 9.1-0.05y-9.1=7.2-9.1 \\ -0.05y=-1.9 \\ \text{divide both sides by 0.05} \\ \frac{-0.05y}{-0.05}=\frac{-1.9}{-0.05} \\ y=38 \end{gathered}[/tex]therefore,
the number of nickles is 38
b) finally, replace the y value into equation (1) and solve for x
[tex]\begin{gathered} x+y=91\Rightarrow equation(1) \\ x+38=91 \\ \text{subtract 38 in both sides} \\ x+38-38=91-38 \\ x=53 \end{gathered}[/tex]so,the number of dimes is 53
the answer is
C: 53
I hope this helps you
