SOLUTION: The sum of 2 numbers is 21.3/4 of one of the number is added to 2/3 of the other gives a sum of 15.Find the two numbers.please with step by step explanation. .

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Question 1152045: The sum of 2 numbers is 21.3/4 of one of the number is added to 2/3 of the other gives a sum of 15.Find the two numbers.please with step by step explanation.
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Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235) (Show Source):
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numbers are x and y, and they add to 21 (3/4) x+y=21 (3/4) so x=21 (3/4)-y
x+(2/3)y=15
therefore x=15-(2/3)y
but from the first, x=21(3/4)-y as well.
since x equals either, they both equal each other
15-(2/3)y=21(3/4)-y
(1/3)y=6 (3/4), and y is 3 times 6 3/4 or 20.25
If one number is 20.25, the other is 1.5 to add to 21 3/4
1.5 + (2/3)20.25=1.5+(2/3)*81/4=1/5(54/4)=1.5+13.5=15

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement
Do what is necessary to get rid of the fractions
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The sum of 2 numbers is 21.3/4
x + y = 21
in the improper fraction form
x + y =
multiply by 4
4x + 4y = 87
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If one of the number is added to 2/3 of the other gives a sum of 15.
x + y = 15
multiply by 3
3x + 2y = 45
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use elimination, multiply the 2nd equation by 2, subtract the 1st equation
6x + 4y = 90
4x + 4y = 87
-------------------subtraction eliminates y, find x
2x + 0 = 3
x = 3/2
x = 1.5 or 1
find y using the 1st simplified equation
4(1.5) + 4y = 87
6 + 4y = 87
4y = 87 - 6
4y = 81
y = 81/4
y = 20.25 or 20
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Check:
1.5 + 20.25 = 21.75 which is 21