One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone plan costs $82 per month for talk and messaging and $3 per gigabyte of data used each month. Let

c represent the total cost in dollars and d represent the amount of data used in gigabytes.

+

Ic=52 + 8d

The system of equations

can be used to represent this situation,

C= 82 + 3d

How many gigabytes would have to be used for the plans to cost the same? What would that cost be?

Both plans would cost s

if

gigabytes of data are used.

Both plans would cost $100 if 6 gigabytes of data are used.

Explanation:

Note: From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:

c = 52 + 8d (1)

c = 82 + 3d (2)

Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:

52 + 8d = 82 + 3d

8d - 3d = 82 - 52

5d = 30

d = 30 / 5

d = 6

Substituting d = 6 into equation (1), we have:

c = 52 + (8 * 6)

c = 52 + 48

c = 100

Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.