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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

ok so i have to figure out how to write this down so i can solve it but i have no idea how to write that down in allgebraic form

### 4 Answers by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
1
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
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
0
L+S=35
3L=4S

L+S=35
3L-4S=0
multiply 1sr equation by 3
3L+3S=105
3L-4S=0
subtract
7S=105
S=15
L=35-15=20

Barry P. | Barry P. - The solution to your Math or Science problemsBarry P. - The solution to your Math or ...
4.9 4.9 (27 lesson ratings) (27)
0
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
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
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!