How many 10c coins did she have at the beginning?

Question

Belinda has 20 coins consisting of 5c coins and 10c coins. If the 5c coins were 10c coins and the 10c coins were 5c coins, she would have 30c more than she has now. How many 10c coins did she have at the beginning?

 

a. 5

b. 7

c. 9

d. 11

 

Answer 1

b.  set up the equation as follows: 5x + 10y = 5y + 10x + 30, and simplify.  Then use x + y = 20 to state that y = 20 - x and substitute into the simplified equation that should be 5y = 5x +30  like this [5(20-x)=5x+30] With distribution, combining like terms and solving for x, we find that x=7.  Thus, y=13.  That equals $1.65 if I use x as the nickels.   So we switch the amounts of coins and end up with $1.35, so there are 7 dimes and 13 nickels.