word problem

Question

Elsie took all of her cans and bottles from home to the recycling center. The number of cans was one more than four times the number of bottles. She  earned 12 cents for each bottle and 10 cents for each can , and ended up earning $2.18 in all . How many cans and bottles did she recycle ? 

Answer 1

Briana, this requires a system of equations.

 

First, let's let c = the number of cans and b = the number of bottles.

 

We are told that c = 4b + 1

 

We also have that .10c + .12b = 2.18

 

We now substitute the "value" for c into the 2nd equation.

 

.10(4b + 1) + .12b = 2.18

.40b + .10 + .12b = 2.18

.52b = 2.08

b = 4

 

Now, c = 4(4) + 1 = 17.

 

So, Elsie recycled 4 bottles and 17 cans.