Question

Patrick wants to buy a new computer. He already has $275 saved and plans to save $125

each month. The price of the computer is currently $1,850, but Patrick expects the price
to drop by $100 each month. Patrick wants to determine the number of months he will
need to save.
.
If x represents the number of months, then write an equation to represent A, the total
amount Patrick saves.
If x represents the number of months, then write an equation to represent C, the cost of
the computer.
.
Use your equations from part “a” and part “b” to determine how many months he will
need to save before he can buy the computer. Show your work or explain how you got
your answer

Answer 1

The answer is below

Explanation:

The equation for a linear function is given as:

y = mx + b

where m is the slope of the function (that is the rate of change), b is the initial value of y when x is 0.

a) Since A represent the total amount saved and x represents the number of months. The relationship between A and x is given by:

A = -100x + 1850

The price reduces by $100 each month, while the initial price is currently $1,850.

B) Since C represent the cost of computer and x represents the number of months. The relationship between C and x is given by:

C = 125x + 275

The price increases by $125 each month, while the initial price is currently $275.

C) To determine the amount time needed before he can buy the computer, we use:

A = C

-100x + 1850 = 125x + 275

125x + 100x = 1850 - 275

225x = 1575

x = 7

Therefore it would take 7 months before he can buy a computer