SOLUTION: How would I figure out this problem? Katie has $880 n $5 bills and $20 bills. If she has four more twenties than fives, how many $20 bills does she have?

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Question 834220: How would I figure out this problem?
Katie has $880 n $5 bills and $20 bills. If she has four more twenties than fives, how many $20 bills does she have?

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
She has a total of $880 in five dollar bills and 20 dollar bills.
she has four more twenties than fives.
how many 20 dollar bills does she have.

let x = number of 5 dollar bills and y = number of 20 dollar bills.

5x + 20y = 880 is your first equation.

this equation is the equation that counts up the total money based on the different bills that she has.

y = x + 4 is your second equation.

this equation give you the relationship between the number of five dollar bills she has and the number of 20 dollar bills that she has.

you have 2 equations that need to be solved simultaneously.

they are:

5x + 20y = 880
y = x + 4

substitute y = x + 4 for y in the first equation to get:

5x + 20(x + 4) = 880

solve for x in this equation.

start with:
5x + 20(x+4) = 880
simplify to get:
5x + 20x + 80 = 880
combine like terms to get:
25x + 80 = 880
subtract 80 from both sides of this equation to get:
25x = 800
divide both sides of this equation by 25 to get:
x = 800 / 25 = 32

x is the number of 5 dollar bills.
since y = x + 4, then y = 36 = the number of 20 dollar bills.

so x = 32 and y = 36

she has 32 five dollar bills and 36 twenty dollar bills.

32 * 5 = 160 dollars
36 * 20 = 720 dollars
720 + 160 = 880 dollars

numbers check out and the solution is good.

she has 32 five dollar bills and 36 twenty dollar bills.