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the sum of two numbers is 35. 3 times the larger number is the same as 4 times the smaller number. find the larger number

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4 Answers

L = larger number
S = smaller number
 
L + S = 35 from which L = 35 - S or S = 35 - L
 
3*L = 4*S
 
Therefore 3*(35 - S) = 4*S
 
105 - 3*S = 4*S
 
Add 3*S to each side
 
105 = S*(4 + 3) = 7S
 
Therefore S = 15
 
L = 35 - S = 35 - 15 = 20
Both approaches are correct but a different one variable approach seem s simpler
 
larger number = L     the other number = 35-L
 
3L=4(35-L)
3L=140-4L
7L=140
L=20
Hi Liz;
I like William's answer.  However, I prefer to only work with one variable.
 
x=larger number
(3/4)x=smaller number
 
(x)+[(3/4)(x)]=35
[(4/4)(x)]+[(3/4)(x)]=35
(7/4)x=35
Let's multiply both sides by 4/7
(4/7)(7/4)x=35(4/7)
x=20
 
If you need the smaller number...
35-20=15
 
To verify...
Does
3(larger)=4(smaller)
3(20)=4(15)
60=60
YES!
 

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