Gabby received change worth $2.10. she received 3 more dimes than nickels and 4 less quarters than nickels. how many of each kind of coins did she receive?

Gabby received

7 nickels

10 dimes

3 quarters

Step-by-step explanation:

Let

x> the number of dimes

y> the number of nickels

z---> the number of quarters

Remember that

1 dime=$0.10

1 nickel=$0.05

1 quarter=$0.25

we know that

0.10x+0.05y+0.25z=2.10 > equation A

x=y+3> equation B

z=y-4 > equation C

substitute equation B and equation C in equation A and solve for y

0.10(y+3)+0.05y+0.25(y-4)=2.10

0.10y+0.30+0.05y+0.25y-1=2.10

0.40y=2.10-0.30+1

0.40y=2.80

y=7 nickels

Find the value of x

x=y+3 > x=7+3=10 dimes

Find the value of z

z=y-4 > z=7-4=3 quarters

therefore

Gabby received

7 nickels

10 dimes

3 quarters