Last year, Pinwheel Industries introduced a new toy.

Question

Last year, Pinwheel Industries introduced a new toy. It cost $1400 to develop the toy and $15 to manufacture each toy. Fill in the blanks below as appropriate.

A.) Give a linear equation in the form C=m n+b that gives the total cost, C, to produce n of these toys:
C=

B.) The total cost to produce n=1750 toys is $.

C.) With $71150, a total of toys can be produced.

Answer 1

Since some numbers are missing, I'll solve with an example.

Let $1400 = the cost to develop the toy. Let $15 = the cost to manufacture each toy.

Since the cost to manufacture the toys is dependent on the quantity, this is our coefficient, and our equation is 1400 + 15x = Cost, where x = the number of toys produced.

to Manufacture 1750 toys, the cost is 1400 + 15(1750) = ?

 How many toys can be manufactured for $71150 ?

 

1400 + 15x = 71150

I'll leave calculations to the student.

Answer 2

A) A linear equation is written in the form y=mx+b, here we are substituting C (total cost) for y and n (number of toys) for x. 

The total cost to develop n toys would be the initial development cost plus the manufacturing cost of each toy. 

m is going to equal the cost to develop a toy because it is multiplied by n, the number of toys.

b is going to equal the development cost because it is a constant and does not change with the number of toys. 

Therefore, C=15n + 1400

 

B) Now take the equation we just wrote for C and plug in n=1750

C= 15(1750) + 1400

C= 26250+1400

C= $27,650

 

C) Now, we use the same equation, but we are given C instead of n.

71150= 15n +1400

71150-1400 = 15n

69750= 15n

Now, divide both sides by 15 to get n by itself:

69750/15= n

n= 4650

 

Answer 3

A.  C = 15n + 1400

 

B.  C = 15*1750 + 1400

C = 26,250 + 1400

c = 27,650

 

C.  71,150 = 15n + 1400

71,150 - 1400 = 15n + 1400 - 1400

69,750 = 15n

n = 4650