Solve appropriate word problems by modeling them with linear equations in two variables.

If the equation representing the cost, C, of producing n tires at Royal Tires Co. can be written as C= mn+ f, where f represents the company’s fixed costs, find the cost of production equation if is is known that it costs $30,000 to produce 1,000 tires while it costs $50,000 to produce 3,000 tires.

The cost of production equation is:

C = 10n + 20000

Solution:

The equation representing the cost, C, of producing n tires at Royal Tires Co. can be written as:

C = mn + f

Where,

C = cost

n = number of tires

f = company's fixed cost

It costs $30,000 to produce 1,000 tires while it costs $50,000 to produce 3,000 tires

Therefore,

30, 000 = m(1000) + f

50, 000 = m(3000) + f

Which is,

1000m + f = 30000 eqn 1

3000m + f = 50000 eqn 2

Subtract eqn 1 from eqn 2

3000m + f = 50000

1000m + f = 30000

( - )

2000m = 20,000

m = 10

Substitute m = 10 in eqn 1

1000(10) + f = 30000

f = 30000 - 10000

f = 20,000

Thus the equation is:

C = 10n + 20000

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt