at the beginning of summer david started adding a little money into a savings account every week. after four weeks balance was $270. at the end of 13 weeks his balance was $405. assume that he put the same amount of money into his account every week and will continue to do so. how long will it take to reach $540

Step-by-step explanation:

Let the initial amount paid by David = x

Let his weekly savings = y

After 4 weeks,

x + 4y = 270 (1)

After 13 weeks,

x + 13y = 405 (2)

(2) - (1) gives

9y = 135

Divide both sides by 9.

y = 15

Substitute in (1), we get,

x + 4 (15) = 270

x + 60 = 270

x = 270 - 60 = 210

Now, let after n weeks, his savings will become 540.

So, x + ny = 540

210 + n (15) = 540

15n = 540 - 210

15n = 330

Divide both sides by 15.

n = 22

Hence, after 22 weeks, the amount will take to reach $540.