Question

Sammy and Hayley are both saving money. Sammy currently has $4000 and is saving $500 a month. Hayley has $7000 right now and is saving $600 a month. Will Sammy ever have the same amount or more money than Hayley. How do you know this? Write an equation in order to prove what your common sense tells you.

Answer 1

In order to know if it is possible that some day Sammy has the same saved money to Hayley, you can write an algebraic equation for the amount of saved money for Sammy and Hayley in the month x, just as follow:

saved money of Sammy for the month x:

4000 + 500x

saved money of Hayley for the month x:

7000 + 600x

You equal the previous expressions to know if there is a value of x in which both Sammy and Hayley will have the same amount of saved money:

4000 + 500x = 7000 + 600x subtract 500x both sides

4000 = 7000 + 100x subtract 7000 both sides

-3000 = 100x divide by 100

-30 = x

The solution to the previous equation was a negative number, but there are no negative months!!!!. Then, the solution is inconsistent and there is no possiblity that Sammy has the same saved money that Hayley.