### Brain Teasers

# Sharing Marbles

Henry and Gretchen each collected marbles, and they were discussing sharing their collections. Here is the conversation they had:

Henry: "If I shared with Lizzie, we would each get 10 marbles."

Gretchen: "If Lizzie shared with Courtney, who has 10 marbles, they would each end up with half as many marbles as I have."

Henry: "Now I know how many marbles we will each end up with if we share."

How many marbles will they each have?

Henry: "If I shared with Lizzie, we would each get 10 marbles."

Gretchen: "If Lizzie shared with Courtney, who has 10 marbles, they would each end up with half as many marbles as I have."

Henry: "Now I know how many marbles we will each end up with if we share."

How many marbles will they each have?

### Answer

15.Using the variables H, G, L, and C to stand for Henry, Gretchen, Lizzie, and Courtney, we get:

(H + L)/2 = 10, so

H + L = 20

(L + C)/2 = G/2, so

(L + 10)/2 = G/2, and

L + 10 = G

(H + G)/2 = (H + L + 10)/2 = (H + L)/2 + 5

Since we know (H + L)/2 = 10, we get (H + G)/2 = 15.

You can also plug in numbers to make this work. If Henry has 10, Lizzie has 10, Courtney has 10, and Gretchen has 20, all of these answers hold. Even if you change the mix (e.g., H = 5, L = 15, C = 10, G = 25), the answer remains the same.

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