Answer:
Number of nickels is 10
Number of dimes is 10
Step-by-step explanation:
Let's assume
number of nickels =n
number of dimes =d
Nicole has 20 coins in her purse
so,
[tex]n+d=20[/tex]
we know that
1 nickel =0.20 dollar
1 dimes =0.10 dollar
total she has $3 in her purse
so, we can get another equation
[tex]0.20n+0.10d=3[/tex]
we get system of equations as
[tex]n+d=20[/tex]
[tex]0.20n+0.10d=3[/tex]
We can isolate n from first and plug into second
[tex]n=20-d[/tex]
[tex]0.20(20-d)+0.10d=3[/tex]
now, we can solve for d
[tex]0.2\left(20-d\right)\cdot \:10+0.1d\cdot \:10=3\cdot \:10[/tex]
[tex]2\left(20-d\right)+d=30[/tex]
[tex]40-d=30[/tex]
[tex]d=10[/tex]
now, we can find n
[tex]n=20-10[/tex]
[tex]n=10[/tex]
So,
Number of nickels is 10
Number of dimes is 10
