PLEASE HELP ASAP

Question

The cost of making 15 tables is $850. The cost of making 24 tables is $940.What is the cost per table? What is the fixed cost (or startup cost) that you need to spend before making the first table? Write a linear equation that tells you the total cost, , of making  tables:    What is the total cost of making 20 tables? $If your total cost is $1,350, how many tables did you make? 

Answer 1

a + 15y = $850

a + 24y = $940

Isolate one of the variables and substitute into the other equation.

a = $850 - 15y

Now plug in

(a) + 24y = $940

($850 - 15y) + 24y = $940

$850 -15y + 24y = $940

$850 + 9y = $940

-$850 -$850

Subtract $850 from both sides to isolate the term with the y variable.

9y = $90

÷9 ÷9

Divide both sides by 9 to isolate the y variable

y = $10

Plug in y to either equation to solve for a

a + 15(y) = $850

a + 15($10) = $850

a + $150 = $850

-$150 -$150

Subtract $150 from both sides to isolate the a term.

a = $700

The fixed startup cost a is $700.

Total cost of making x tables.

C(x) = $700 + (x • $10)

Total cost of making 20 tables?

C(20) = $700 + (20 • $10) = $900

If total cost is $1350 how many tables were made?

C(x) = $1350 = $700 + (x • $10)

-$700 -$700

Subtract $700 from both sides of the equation to isolate the x term.

$650 = x • $10

÷$10 ÷$10

Divide both sides by $10 to isolate the x variable.

65 = x

So there are 65 tables made if the total spent is $1350 in costs.