word problems?

Question

eight girls want to rent a gym for basketball practice each girl will pay one-eigth of the monthly rent. If they could find two more girls to share the cost of the monthly rent, each of them would pay $2.50 less. What is the monthly rent?

Answer 1

Let monthly rent = R. According to the problem, this is what you are solving for.

So eight girls each pay 1/8th of the rent. Let the price each girl pays = p

8p = R

Now you know that if you had 2 more girls (i.e., ten girls) each would pay $2.50 LESS, or p-2.50. The rent stays the same regardless of how many girls split it up, so only the left side changes.

10(p-2.5) = R --> (10 girls times the original payment less $2.50 each). Simplify to 10p - 25 = R

Now you have two equations and 2 variables, so you can solve as a system of equations. Since they are both equal to R, they are equal to eachother.

10p - 25 = 8p

2p = 25
p = 12.50

**CAUTION** this is NOT what the question asked. Remember you are solving for R, so go back and plug it in

8p = R
8(12.5) = $100.00 (don't forget the units)

And just to make sure:

10p-25 = R
10(12.5) - 25 = $100.00

So the monthly rent is $100.00.

Answer 2

If each of the eight original girls will save $2.50, this means that the two new girls will be making up this amount; so together the new girls will be paying $2.50 X 8 = $20.00, or $10.00 apiece. But the cost is shared equally by all, so the other eight girls will also be paying $10.00 each. Thus the monthly rent is $10.00 X 10 = $100.00. To check this, notice that $100.00 split eight ways is $12.50 each, so the eight original girls will indeed be saving $2.50 each if they find two more to share the rent

Answer 3

The monthly rent is $100.

Here's how to compute: we denote the monthly rent with x and have the following equation to solve:

x/(8+2) = x/8 - 2.5
Multiply that by 40 and get:
4x=5x-100
x=100

Answer 4

I suggest you set up an equation with 2 unknowns (payment and monthly rent) from the first sentence.
Then set up one from the additional data with the same 2 unknowns. Solve second for the payment and substitute into the first.

Then do the math and you got the answer.

Answer 5

100