How many of each coins do they have?

Question

A man has 27 coins, all of which are pennies, Nickel, dimes and quarters. He has five more dimes than pennies and three times as many quarters as nickels. If the total value of his change is $3.45, how many of each does he have?

Answer 1

First set up a key

coin type         number of coins      value in dollars

penny                   x                           .01x

nickel                   y                            .05y

dime                    x+5                        .10(x+5)

quarter                  3y                         .25(3y)

 

x+y+(x+5) +3y = 27 coins in total

.01x+.05y+.10(x+5) + .25(3y) = 3.45

 

Simplifying you get

2x+4y = 22            divide by 2

.11x+.8y = 2.95     multiply by 100 to get rid of decimals

 

x+2y = 11            multiply by -11

11x+80y = 295

 

-11x - 22y = -121

 11x + 80y = 295       add together

 

         58y   = 174    divide by 58

            y    = 3

 

plug into easier equation to get x

 

x+2y=11.......x+2(3)=11.......x=5

 

Substituting back into your key you get

5 pennies, 3 nickels, 10 dimes and 9 quarters.

 

That's 27 coins and the value is .05+.15+1.00+2.25=$3.45

 

So our answer is correct.

 

Hope this helped