Question

Tyler has $9.70 in dimes and quarters. The number of quarters is eight more than four times the number of dimes. How many of each coin does he have?

Answer 1

Tyler has 7 dimes and 36 quarters.

Explanation

Suppose, the number of dimes is $x$

As the number of quarters is eight more than four times the number of dimes, so the number of quarters $=4x+8$

Value of one dime is $0.10 and value of one quarter is $0.25

Given that, total value of all dimes and quarters is $9.70

So, the equation will be....

$0.10x+0.25(4x+8)=9.70\\ \\ 0.10x+1x+2=9.70\\ \\ 1.10x+2=9.70\\ \\ 1.10x= 9.70-2\\ \\ 1.10x=7.70\\ \\ x=\frac{7.70}{1.10}=7$

So, the number of dimes is 7 and the number of quarters $=4(7)+8=28+8=36$