2017 AMC 10B Problem 5

Below is the professionally curated solution for Problem 5 of the 2017 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 10B solutions, or check the answer key.

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Concepts:system of equations linear equation

Difficulty rating: 900

Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?

$10$

$20$

$30$

$40$

$50$

Solution:

Let the number of cherry jelly beans be $c$ and let the number of blueberry jelly beans be $b$

Then, we know $b = 2c$ $b-10=3(c-10)$ from the first and second statements respectively.

Therefore, $2c-10 = 3c-30$ $c=20.$ This means that $b = 2\cdot 20=40.$

Thus, the correct answer is D .

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