Question

Alex has $20, and Ellen has $12. Alex is saving $3 per day, and Ellen is saving $5 per day. After how many days will Alex and Ellen have the same amount of money? Write and solve a system of equations

Answer 1

By setting up a system of linear equations using the starting amounts and savings rates for Alex and Ellen, we found that after 4 days, they will have the same amount of money.

Step-by-step explanation:

To solve the problem, let's create a system of equations based on the information provided. Let x represent the number of days after which they will have the same amount of money. Alex starts with $20 and saves $3 per day, while Ellen starts with $12 and saves $5 per day. Thus, for Alex, the total amount of money after x days will be represented by the equation A(x) = 20 + 3x. For Ellen, the total amount of money after x days will be represented by the equation E(x) = 12 + 5x.

Since we're looking for the point where they have the same amount of money, we can set these equations equal to each other:

20 + 3x = 12 + 5x

Moving all the variable terms to one side and constants to another side, we get:

3x - 5x = 12 - 20

This simplifies to:

-2x = -8

Divide both sides by -2 to find the value of x:

x = 4

Therefore, after 4 days, Alex and Ellen will have the same amount of money.