Question

A student solved this problem by making a table.

Arturo has $120. Max has $90. In how many years will they both have the same amount of money if Arturo saves $90 per year and Max saves $100?


Arturo $120 $210 $300 $390
Max $90 $190 $290 $390
Year 0 1 2 3


Here is a problem that can also be solved by making a table.

Amira has $80. Sasha has $40.

In how many months will they both have the same amount of money if Amira saves $40 per month and Sasha saves $50?

how many months is it?

Answer 1

Hello! I can help you with this! For this problem in order to find the amount of months it will take for them to have the same amount of money, we can write and solve an equation.

1. Okay. Amira has $80, and saves $40 a month. Max has $40 and saves $50 a month We have the numbers, so we can write the equation. Set it up like this:

80 + 40x = 40 + 50x

We set it up like this, because each girl has some money, but they're saving more to add to the total. Let's start solving. Subtract 40x from both sides. 40x - 40x cancels out. 50x - 40x is 10x. That shortens to 80 = 40 + 10x. Subtract 40 to get both sides by themselves. 40 - 40 cancel out. 80 - 40 is 40. That simplifies to 40 = 10x. Now, divide each side by 10 to isolate the x. 10x/10 cancel out. 40/10 is 4. Let's test this out and see if it works. 40 * 4 is 160. 160 + 80 is 240. 50 * 4 is 200. 200 + 40 is 240. 240 = 240. There. x = 4. Amira and Sasha will have the same amount of money in 4 months.