Answers:
- Ally gets 100 pounds
- Barry gets 150 pounds
- Cat gets 250 pounds
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Work Shown:
x = some positive real number
2x = amount Ally gets
3x = amount Barry gets
5x = amount Cat gets
Note that the ratio 2x:3x:5x reduces to 2:3:5 after dividing all parts by x.
Add up the parts and you should get a sum of 500 pounds. Solve for x.
2x+3x+5x = 500
10x = 500
x = 500/10
x = 50
Based on that x value, we then can say:
- 2x = 2*50 = 100 pounds is what Ally gets
- 3x = 3*50 = 150 pounds is what Barry gets
- 5x = 5*50 = 250 pounds is what Cat gets
As a check, 100+150+250 = 500.
Also, note that the ratio 100:150:250 fully reduces to 2:3:5 after dividing all parts by the GCF 50.
Those two facts help confirm our answers.