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Answers
The ratio x:y:z is 10:5:3
Ali got 20,000
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Explanation:
Let
- x = amount Ali got
- y = amount Ben got
- z = amount Chris got
Those amounts add to 36,000
x+y+z = 36,000
We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps
x+y+z = 36,000
2y+y+z = 36,000
3y+z = 36,000
We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.
3y+z = 36,000
5z+z = 36,000
6z = 36,000
z = (36,000)/6
z = 6,000
This tells us that Chris got 6,000
Use this to find y
3y = 5z
3y = 5*6,000
3y = 30,000
y = (30,000)/3
y = 10,000
Ben received 10,000
Lastly, determine x.
x = 2y
x = 2*10,000
x = 20,000 which is the amount Ali got.
The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.
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Check:
Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000
which helps confirm the answer.
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