Question

A designer builds and sells small chairs and large chairs. The cost of material is $10 for each small chair and $15 for each large chair. The selling price is $22 for a small chair and $51 for a large chair. Part A The designer spends $305 on material to make chairs. The designer makes 8 more small chairs than large chairs. Write a system of equations that can be used to determine s , the number of small chairs, and t , the number of large chairs, the designer makes. How many small chairs did the designer make? Enter your answers in the space provided. Enter only your answers.

Answer 1

The equations are:

15s + 10t = 305...............(1)

s + 8 = t ...........................(2)

The number of small chairs is 9

The number of large chairs is 17

Explanation:

- Cost of materials for one small chair = $10

- Cost of materials for one large chair = $15

- Selling price for one small chair = $22

- Selling price for one large chair = $51

Now, The designer spends $305 on material to make chairs. The designer makes 8 more small chairs than large chairs.

Let one small chair be s, and one large chair be t.

Then

Number of chairs:

15s + 10t = 305...............(1)

But again, there are 8 more small chairs than large chairs, so,

s + 8 = t ...........................(2)

Solving (1) and (2) simultaneously, we have the number for each sizes of chair.

Using (2) in (1)

15s + 10(s + 8) = 305

15s + 10s + 80 = 305

15s + 10s = 305 - 80

25s = 225

s = 225/25

s = 9

Since t = s + 8

t = 9 + 8 = 17

So s = 9, t = 17