Tina and jeff are both saving money in their piggy banks. tina has 100 dollars already and saves $5 every week jeff has $28 dollars already and saves $8 each week. how many weeks will it take until they have saved the same amount of money.?

Given the word problem we know how much Tina and Jeff are saving.  Broken down into equations they are as follows:

Tine: 100 + 5x

Jeff:  28 + 8x

The first value represents the amount each has saved already and the second value is the amount saved per week, with x representing weeks.  Since we know the value is going to match ("how many weeks will it takesame amount of money"), we know we can equal the the equations since x will be constant.  So we end up with this:

100 + 5x = 28 + 8x   At this point we need to isolate x to find the value

100 = 28 + 3x   (Subtract $5x from each side)

72 = 3x   (Subtract $28 from each side)

24 = x   (Divide 72 by 3 to end up with our x value (weeks)

Now that we have our x value representing weeks, lets plug our answer back into the original two equations to double check our work.

100 + 5(24) =        100 + 120 = 220

28 + 8(24) =          28 + 192 = 220

Both answers match at 220 equaling the same amount.  The answer, after being double checked, is 24 weeks.

(-5,-28)

i graphed to on desmos.