2017 AMC 10B Problem 5

Question

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

Answer: D

Concepts:system of equations linear equation

Difficulty rating: 900

Small hint:

Let the original cherry and blueberry counts be variables

Big hint:

Use one equation before and one equation after eating the jelly beans

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 .