Andrew M. answered • 02/19/18
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
One number is 3 more than twice the same number if their sum is 21, what are the numbers?
Note: The number cannot be 3 more than twice the SAME number.
It can be 3 more than twice another number.
x = 2y + 3
x + y = 21
Replace x with 2y + 3 in 2nd equation
2y + 3 + y = 21
3y + 3 = 21
3y = 18
y = 6
x = 2y + 3 = 15
The numbers are 6 and 15
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One number is four less than twice ANOTHER number.
Let y be the smaller number:
x = 2y - 4
If the smaller number is divided by 2, and the larger number is divided by 3,
the sum of quotients is 8. What are the numbers?
y/2 + x/3 = 8
y/2 + (2y-4)/3 = 8
multiply through by 6
3y + 2(2y-4) = 48
3y + 4y - 8 = 48
7y = 56
y = 8
x = 2y-4 = 12
The numbers are 8 and 12
Andrew M.
Since I had fractions with denominators of 2 and 3, I multiplied all terms by the
lowest common multiple of 2 and 3 which is 6 in order to clear out the fractions.
Note: If a = b then an = bn
If a/2 = b/3 .... then 6(a/2) = 6(b/3) giving me 3a = 2b
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This is how it worked in the problem you posted:
y/2 + (2y-4)/3 = 8
multiply through by 6
6[y/2 + (2y-4)/3] = 6(8)
6(y/2) + 6[(2y-4)/3] = 48
3y + 2(2y-4) = 48
3y + 4y - 8 = 48
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02/19/18
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02/19/18