SOLUTION: Moe has 20% more marbles than Curly. Curly has 20% more marbles than Larry. If Moe gives Curly some marbles such that they end up with an equal number of marbles, Curly will have 2

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Question 1199578: Moe has 20% more marbles than Curly. Curly has 20% more marbles than Larry. If Moe gives Curly some marbles such that they end up with an equal number of marbles, Curly will have 24 more marbles than Larry. How many marbles does Larry have?
Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

x = amount of marbles Larry has
x is some positive whole number

20% of x = (20/100)x = 0.20x

Curly has 20% more compared to Larry, which means x+0.20x = 1.20x is the amount Curly starts off with.
Think of 1.20 as 120%

Moe has 20% more compared to Curly, which means Moe has 1.20*(1.20x) = 1.44x marbles.

Moe = 1.44x
Curly = 1.20x
Larry = x

m = amount of marbles Moe gives to Curly
Moe's count goes from 1.44x to 1.44x-m
Curly's count goes from 1.20x to 1.20x+m

After Moe gives those marbles to Curly, these two people will have the same number of marbles.

Which means we know that:
1.44x-m = 1.20x+m

Let's solve for m
1.44x-m = 1.20x+m
1.44x-1.20x = m+m
0.24x = 2m
m = 0.24x/2
m = 0.12x

At this point, Curly's marble count (1.20x+m) is 24 larger compared to Larry's count (x)

Curly = Larry + 24
1.20x+m = x + 24
1.20x+0.12x = x + 24 .... plug in m = 0.12x
1.32x = x+24
1.32x-x = 24
0.32x = 24
x = 24/0.32
x = 75
Larry has 75 marbles.

An alternative equation to solve would be: 1.44x-m = x+24
I'll let the student solve this. You should arrive at x = 75.

Curly = 1.20x = 1.20*75 = 90
Moe = 1.44x = 1.44*75 = 108
Or,
Moe = 1.20*(Curly) = 1.20*90 = 108

Summary:
Moe = 108
Curly = 90
Larry = 75
Moe's and Curly's count is before Moe gives over those m number of marbles.

Let's calculate m
m = 0.12x = 0.12*75 = 9
This is the amount of marbles Moe gives to Curly.
Moe = 108-9 = 99
Curly = 90+9 = 99
These two men now have the same number of marbles, which helps confirm the answer.

Also, take note that these two men each have 24 more marbles compared to Larry (since 75+24 = 99). This adds further confirmation we have the correct answer.

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Answer: Larry has 75 marbles

Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
x, how many marbles Larry has
g, how much Mo gives to Curly

Without showing some of the initial arithmetic, STARTING GIVING SOME Mo 1.44x 1.44x-g Curly 1.2x 1.2x+g Larry x 1.2x+g-x=24

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