Question

She needs to buy at least 100 chairs. Chairs with arms cost $80. Chairs without arms cost $70. Ms. Robinson can spend, at most, $7,500 on chairs.

Answer 1

50 chairs with arms and 50 without arms will cost $7500

Explanation:

Create two equations using the given information. The unknowns are :

W = Number of chairs with arms

N = Number of chairs with No arms

First equation (associated with the total number of chairs to buy):

W + N = 100

Second equation (associated with the amount to spend):

80 W + 70 N = 7500

Solving: solve for W in the first equation: W = 100 - N

Use it to substitute for W in the second equation:

80 (100 - N) + 70 N = 7500

8000 - 80 N + 70 N = 7500

subtract 8000 from both sides and combine

- 10 N = - 500

Divide both sides by -10 in order to solve for N

N = -500 / (-10) = 50

Now use this value in the substitution equation to solve for W:

W = 100 - 50 = 50

So the person can buy 50 chairs with arms and 50 chairs without arms paying for them $7,500.