Question

James has dimes and quarters saved up in his change jar . he has a total of 162 coins totaling $31.20 , find the numbers of dimes and quarters

Answer 1

62 dimes and 100 quarters

Step-by-step explanation

Step 1

Let

1 dime= $0.10

1 quarter=$0.25

x= number of dimes

y= number of quarters

he has a total of 162 coins ,then

`x+y=162\text{ Equation (1)}`

Also, the coins total is $31.20,then

`0.10x+0.25y=31.20\text{ Equation (2)}`

Step 2

find x and y using equation (1) and (2)

i) isolate x in equation(1) then replace in equation (2)

`\begin{gathered} x+y=162 \\ \text{subtrac y in both sides} \\ x+y-y=162-y \\ x=162-y \\ \text{now, replace in equation(2)} \\ 0.10x+0.25y=31.20 \\ 0.10(162-y)+0.25y=31.20 \\ 16.2-0.10y+0.25y=31.20 \\ 0.15y+16.2=31.20 \\ \text{subtract 16.2 in both sides} \\ 0.15y+16.2-16.2=31.20-16.2 \\ 0.15y=15 \\ \text{divide both sides by 0.15} \\ (0.15y)/(0.15)=(15)/(0.15) \\ y=100 \end{gathered}`

so, he has 100 quarters

Step 3

replace y=100 in equation (1) to find x

`\begin{gathered} x+y=162 \\ x+100=162 \\ \text{subtract 100 in both sides} \\ x+100-100=162-100 \\ x=62 \end{gathered}`

he has 62 dimes,

I hope this helps you