algebra 1 word problem

Question

devin volunteers to bring 80 water bottles to a swim meet. he has 10 water bottles in the fridge at home. the store sells cases of water bottles that contain 24 bottles each.

A) write an equation to figure out how many cases Devin needs to buy to have enough water bottles for the meet. Hint: figure out the variable first

B) solve the equation in A

Answer 1

Devin needs 80 water bottles in total.

He has 10 bottles right now -> the initial amount of bottles.

1 case = 24 bottles, A cases = (24 * A) bottles. (A is number of cases)

He needs to buy enough water bottles -> at least 80 water bottles.

24 * A + 10 = 80

24 * A = 70

A = 70 / 24 = 35 / 12 =2.916666666666...

He cannot buy 2.916666666 cases, he needs to buy 3 cases to have enough water bottles

Answer 2

A)

b = 24c + 10

where b is the number of bottles he will have, and c is the number of cases of water he buys. Note that each case has 24 bottles and that he has 10 bottles to start with.

B)

Set b = 80:

80 = 24c + 10

Subtract 10 from both sides of the equation:

70 = 24c

Divide both sides by 24:

c = 2.9 (rounded to 2 decimal places)

It is not likely that the store will sell fractional cases, so we need to buy 3 cases.

That will give us 3 * 24 = 72 bottles.

Adding the 10 we already had gives us 82 bottles, which gives us enough to spare.