They will have the same amount of money after 10 months
They will have $250 at this point
Step-by-step explanation:
The given is:
- Sarah has $400 in her bank account and she has to pay $15 each month to her parents for her cell phone bill
- Darius has $50 and saves $20 each month from his job
We want to find when Sarah and Darius will have the same amount of money and how much they will have at this point
Assume that they will have the same amount of money in x months
∵ Sarah has $400 in her bank account
∵ She has to pay $15 each month to her parents for her cell phone bill
∵ She do that for x months
∴ Her amount of money = 400 - 15(x)
∴ Her amount of money = 400 - 15 x ⇒ (1)
∵ Darius has $50
∵ He saves $20 each month from his job
∵ He do that for x months
∴ His amount of money = 50 + 20(x)
∴ His amount of money = 50 + 20 x ⇒ (2)
∵ They have the same amount of money in x months
- Equate (1) and (2) to find the value of x
∴ 400 - 15 x = 50 + 20 x
- Subtract 50 from both sides
∴ 350 - 15 x = 20 x
- Add 15 x to both sides
∴ 350 = 35 x
- Divide both sides by 35
∴ 10 = x
They will have the same amount of money after 10 months
Substitute the value of x in (1) or (2) to find the amount of money they will have at this point
∵ The amount of money = 400 - 15(10)
∴ The amount of money = 400 - 150
∴ The amount of money = $250
They will have $250 at this point
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