Question

Jane had 275 stickers, which she gave to her friends. Each friend got five more stickers than the friend before. If the first friend got 5 stickers, how many friends got stickers from Jane?

Answer 1

10 friends.

Explanation:

Givens

Sum = 275

a1 = 5

d = 5

n = ?

Formula

Sum = ( (2*a1) + (n - 1)*d) * n / 2 Substitute the knows.

Solution

Sum = ( 2 * 5 + (n - 1)*5 ) * n/2 Combine on the right

275 = (10 + (n - 1)5 ) n/2 Multiply by 2 and remove the brackets.

550 = (10 + 5n - 5) * n Combine

550 = (5 + 5n ) * n Remove the brackets

550 = 5n + 5n^2 Subtract 550 from both sides.

5n^2 + 5n - 550 = 0 Divide by 5 (all terms are divisible by 5)

n^2 + n - 110 = 0 Factor

(n + 11)(n - 10) = 0

The only root that has any meaning is n - 10 = 0

n + 11 means Jane has - 11 friends. That has no meaning at all.

n - 10 = 0

n = 10

She had 10 friends who got stickers.