Jaclyn had $120 and saved and earns $40 each month in alowance. Pedro has $180 saved and earns $20 in a month in allowance. If they both save thir entire allowaces how long will it take before jaclyn and pedro have the same amount of money?

Jaclyn had $120 saved and earns $40 each month in allowance. This means that the number of months that it took Jacklyn to save $120 would be the total amount saved / the amount saved. This becomes 120/40 = 3 months

Since the monthly amount earned is constant, total amount A, earned by Jaclyn in n number of months will be

A(n) = 40n

She had already earned $120 in 3 months, so

A(n+3) = 40n + 120

Pedro has $180 saved and earns $20 in a month in allowance. This means that the number of months that it took Pedro to save $180 would be the total amount saved / the amount saved. This becomes 180/20 = 9 months.

Since the monthly amount earned is constant, total amount B, earned by Pedro in n number of months will be

A(n) = 20n

She had already earned $180 in 9 months, so

B(n+9) = 20n + 180

They would earn the same amount when

A(n+3) = B(n+9) . therefore

40n + 120 = 20n + 180

40n - 20n = 180 - 20

20n = 60

n = 60/20 = 3 months