Question

5) On each birthday Rosa gets as many roses as she is old in years. She still has all the dried flowers and there are now 120 of them. How old is she? A) 10 B) 12 C) 14 D) 15 E) 20

Answer 1

Answer:

D) 15

Step-by-step explanation:

This is an arithmatic progression.

The formula for the sum of arithmatic progression is

$s = \frac{n}{2} (2a + (n - 1)d)$

where d is the common difference between successive terms and a is the first term. By applying this formula,

$120 = \frac{n}{2} (2(1) + (n - 1)(1)) \\ 120 = \frac{n}{2} (1 + n) \\ n(1 + n) = 240 \\ n {}^{2} + n - 240 = 0 \\ (n - 15)(n + 16) = 0 \\ n = 15 \: or \: n = - 16(reject)$