Barney and Betty break into a parking meter with $5.05 in dimes and quarters in it, and agree that Barney get all the dimes, and Betty will get all the quarters. Barney ends up with five more coins than Betty. How much money did each get?

So remember that a quarter=25 cents and a dime=10 cents so

represent q=# of quarters

d=# of dimes

so barney gets dimes so replace barney with d and betty with q

barney get 5 more coins than betty

d=5+q

total=5.05=0.25q+0.10d since each is worth 0.25 and 0.10 so we have

d=5+q and 5.05=0.25q+0.10d

subsitue (5+q) for d

5.05=0.25q+0.10 (5+q)

distribute

5.05=0.25q+0.50+0.10q

add like terms

5.05=0.35q+0.50

subtract 0.50 from both sides

4.55=0.35q

divide both sides by 0.35

13=q

subsitute

d=5+q

d=5+13

d=18

barney got 18 coins and betty got 13 coins