Question

What two numbers have a sum of 24 and have a quotient of 3?

Answer 1

1st number is x
then the other will be 3x
3x+x=24
4x=24
x=6-first number
2nd is 3*6=18

Answer 2

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Define x and y :
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Let one number be x.
Let the other number be y.

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Construct equation :
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x + y = 24
x ÷ y = 3

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Solve for x and y :
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x + y = 24 ------------------- (1)
x ÷ y = 3 --------------------- (2)

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From equation 1 :
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x + y = 24
x = 24 - y 

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Sub x = 24 - y into 2 :
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x ÷ y = 3               // Equation 2
(24 - y) ÷ y = 3      // Sub x = 24
24 - y = 3y            // Multiply by y on both sides
24 = 4y                 // Add y to both sides
4y = 24                 // Switch side, make y the subject
y = 6                     // Divide by 4 on both sides

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Sub y = 6 into equation 1 :
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x + y = 24            // Equation 1
x + 6 = 24            // sub y = 6
x = 18                  // Take away 6 from both sides

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Find the two numbers :
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One number = x = 18
The one number = y = 6

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Answer: The two numbers are 18 and 6.
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