Que: Mandy sold 720 apples in 15 days. If the number of apples she sold increased by 5 each day.....

[Max@Math Revolution]

Que: Mandy sold 720 apples in 15 days. If the number of apples she sold increased by 5 each day, how many apples did she sell on the 8th day?

A. 8
B. 51
C. 43
D. 35
E. 53

[Max@Math Revolution]

Solution: We have to find the number of apples did Mandy sell on \(8^{th}\) day.

Given: Mandy sold 720 apples in 15 days and the number of apples she sold increased by 5 each day

1st day: x
2nd day: x + 5
3rd day: x + 5 + 5 = x + 2*5 .
.
.
15th day: x + 14*5

=> x + (x + 5) + (x + 2*5) + ….+(x + 14*5) = 720

=> 15x + 5 + 2*5 + …..+ 14*5 = 720

=> 15x + 5( 1 + 2 + …. + 15) = 720

=> 1 + 2 + 3 + 4 +…..+ n = \(\frac{n\left(n+1\right)}{2}\)

=> 15x + 5[\(\frac{15\cdot16}{2}\)] = 720

=> 15x + 600 = 720

=> 15x = 120

=> x = 8

=> ∴ \(8^{th}\) day = x + 7*5 = 8 + 35 = 43

Therefore, C is the correct answer.

Answer C