Tyler has 7 dimes and 36 quarters.
Explanation
Suppose, the number of dimes is [tex]x[/tex]
As the number of quarters is eight more than four times the number of dimes, so the number of quarters [tex]=4x+8[/tex]
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....
[tex]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[/tex]
So, the number of dimes is 7 and the number of quarters [tex]=4(7)+8=28+8=36[/tex]
