# MATH

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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 -

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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