Question

Jonah has collected 91 coins worth $7.20 in his piggy bank. His collection only includes dimes and nickels. How many dimes are there in Jonah's piggy bank?a: 36b: 38c: 53d: 72

Answer 1

the number of nickles is 38

C: 53

Step-by-step 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

`x+y=91\Rightarrow equation(1)`

b) it worth $7.20,

hence

`0.1x+0.05y=7.20\Rightarrow equation(2)`

Step 2

solve the eqautions

a) isolate x in equation and replace the result in equation (2)

`\begin{gathered} x+y=91\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=91-y \\ x=91-y \end{gathered}`

replace in equation (2)

`\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} \\ (-0.05y)/(-0.05)=(-1.9)/(-0.05) \\ y=38 \end{gathered}`

therefore,

the number of nickles is 38

b) finally, replace the y value into equation (1) and solve for x

`\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}`

so,the number of dimes is 53

the answer is

C: 53

I hope this helps you