Let us assume that number of dimes is x and number of nickels is y.
We have been given that total value of the money is 85 cents. Therefore, we can express an equation as
[tex]10x+5y=85[/tex]
Further, we are given that number of dimes is four more than the number of nickels. Using this sentence, we can write another linear equation as:
[tex]x=y+4[/tex]
In order to solve this system of linear equations, we can plug [tex]x=y+4[/tex] in the first equation:
[tex]10(y+4)+5y=85[/tex]
[tex]10y+40+5y=85[/tex]
[tex]15y=45[/tex]
[tex]y=3[/tex]
Since [tex]x=y+4[/tex], therefore, we can set up:
[tex]x=3+4[/tex]
[tex]x=7[/tex]
Therefore, Taylor has 7 dimes and 3 nickels.
