Posted by **Anonymous** on Tuesday, September 17, 2013 at 7:31pm.

Mira, Noreen and Olivia each have 20 pretzels. After Mira gives Noreen p pretzels and Olivia gives q pretzels, the ratio of Mira's pretzels to Noreen's pretzels to Olivia's pretzels is 5:9:6. What is p + q?

- MATH -
**Jai**, Tuesday, September 17, 2013 at 7:39pm
Mira: 20

Noreen: 20

Olivia: 20

After they give pretzels,

M: 20 - p

N: 20 + p + q

O: 20 - q

What we can do here is add all of them and equate them to the sum of the ratio multiplied by a certain factor, say x:

(20 - p) + (20 + p + q) + (20 - q) = (5+9+6)x

The p's and q's will all be cancelled and we're left with,

20 + 20 + 20 = 20x

60 = 20x

x = 3

Therefore, after they give their pretzels, they have

M: 5*3 = 15

N: 9*3 = 27

O: 6*3 = 18

Thus,

15 = 20 - p

p = 20 - 15

p = 5

18 = 20 - q

q = 20 - 18

q = 2

Therefore, p + q = 7.

Hope this helps~ :3

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