SOLUTION: please help me answer the following question, showing all your work and at least 5 sentences explaining HOW and WHY you arrived at your answer. You and your best friend are savi

Question 1006134: please help me answer the following question, showing all your work and at least 5 sentences explaining HOW and WHY you arrived at your answer.
You and your best friend are saving money for a shopping trip you would like to take. Your best friend begins with $5, and saves $11 each week. You begin with $23, and save $8 each week. Write an equation to represent when you and your friend will have saved the same amount of money. How much money will you each have saved?

Found 2 solutions by rothauserc, josgarithmetic:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the number of weeks you and your friend save, then
your friend = 5 + 11x
the total amount your friend saves equals 5 which he starts with plus 11 times x
you = 23 + 8x
the total amount you save equals 23 which you start with plus 8 times x
we are looking for the value of x which makes your friend's savings equal you savings
we do this by setting the equations equal to each other
5 +11x = 23 +8x
subtract 5 from both sides of =
11x = 18 +8x
subtract 8x from both sides of =
3x = 18
divide both sides of = by 3
x = 6, therefore
In six weeks you and your friend will have saved $71
*****************************************************************************
check the answer by substituting 6 for x
5 +(11 * 6) = 23 +(8 * 6)
5 + 66 = 23 + 48
71 = 71
our answer checks

Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
These are the money quantities saved for w number of weeks.
Friend:
Person:

Those are linear equations in the variable, w. This variable is for Whole number values.

When both savings equal?

, when both have the same amount of money saved.
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