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Define x :
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Let x be the smaller number.
Let y be the larger number.
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Construct the equations :
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Three times the larger number is equal to 4 times the smaller ones.
⇒ 3y = 4x
The sum of the numbers is 21
⇒ x + y = 21
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Solve for x and y :
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3y = 4x -------------------- (1)
x + y = 21 ----------------- (2)
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From equation (2) :
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x + y = 21
x = 21 - y
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Substitute x = 21 - y into equation (1) :
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4y = 3( 21 - y)
4y = 63 - 3y
7y = 63
y = 9
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Substitute y = 9 into equation 2 :
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x + y = 21
x + 9 = 21
x = 21 - 9
x = 12
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Answer : The two numbers are 9 and 12.
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