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.

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

Step-by-step 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