Question

PLEASE HELP!!!!!!!!!!!!!!!!

Jack wants to buy an electric guitar. He began the the year with some money saved to buy the guitar, and each week he adds a fixed amount to his savings. If y represents the total amount Jack has saved after x weeks, which of the following situations is represented by the table below?


A.

Jack initially had $45 saved, and the amount is increasing at a rate of $15 per week.

B.

Jack initially had $45 saved, and the amount is increasing at a rate of $30 per week.

C.

Jack initially had $75 saved, and the amount is increasing at a rate of $15 per week.

D.

Jack initially had $75 saved, and the amount is increasing at a rate of $30 per week.

Answer 1

15$/week

Initial amount = 45$

Correct Option= A

Explanation:

The equation that represents the total amount Jack has saved is

y = Ax +B

where B is the initial amount saved.

We know that after two weeks, he has saved 75$

75$ = 2*A +B

We know that after four weeks, he has saved 105$

105$ = 4*A +B

With this, we have a system of two equations with two unknowns,

We solve for A and B

B = 75$ - 2*A

105$ = 4*A + 75$ - 2*A

A = 15$/week

B = 75$ - 2 weeks*(15$/week) = 45$