Answer: it will take 3 months to save the same amount
Explanation:
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