Answer:
Man has 9 Nickels and 7 dimes.
Step-by-step explanation:
Let Number of dimes be x
and Number of Nickels be y
As Per given data he has two more nickels than dimes.
[tex]y= 2+x\\[/tex]
As we know that
1[tex]\$[/tex] = 100 cent
1 nickel is worth = 5 cents = [tex]\frac{5}{100}[/tex]= 0.05[tex]\$[/tex]
1 dime is worth = 10 cents = [tex]\frac{10}{100}[/tex] 0 .1[tex]\ $[/tex]
According to given data he has [tex]\$\ 1.15[/tex] total nickel and dimes
So the equation becomes,
[tex]0.05y+0.1x=1.15[/tex]
but [tex]y= 2+x[/tex]
[tex]0.05(2+x)+0.1x=1.15\\0.1+0.05x+0.1x=1.15\\0.1+0.15x= 1.15\\0.15x= 1.15-0.1\\0.15x=1.05\\x=\frac{1.05}{0.15}= 7[/tex]
Substituting value of x in equation [tex]y = 2+x[/tex] we get
[tex]y= 2+7 =9[/tex]
Man has 9 Nickels and 7 dimes.
