Math question on Linear Equations?

Question

I'm having troulbe figuring this out
Solve for S, M, L
120s+150m+174L=36000
30s+36m+48L=9000
4s+4m+4L=1000

Thanks for any help,
Scott

Answer 1

Lets take the first 2

120s+150m+174L=36000
-4(30s+36m+48L=9000) <---multiply whole thing by -4 to get rid of s

120s+150m+174L=36000
-120s-144m-192L=-36000 <---now added both together

6m - 18L = 0 solve for m
6m = 18L
m = 3L

Do the same for 2nd and third ones but try to get s = L
30s+36m+48L=9000
-9(4s+4m+4L=1000) multiply by -9 to get rid of m

30s+36m+48L=9000
-36s-36m-36L=-9000 <--add together

-6s + 12 L = 0
-6s = -12L
s = 2L

Now plug both answer into the last one

4(2L) + 4(3L) + 4L = 1000
8L + 12L + 4L = 1000
24L = 1000
L = 41 2/3 or 125/3
So plug this into s = 2L and m = 3L to get answers.

L= 125/3, s= 250/3, m=125 Plug into any of the equations to check your answers. I'll use the third one

4 (250/3) + 4 (125 ) + 4(125/3) =? 1000
(1000/3) + 500 + (500/3) =? 1000
(1500/3) + 500 =? 1000
500 + 500 =? 1000
1000 = 1000 CHECK

Answer 2

(1) 120s+150m+174L=36000
(2) 30s+36m+48L=9000
(3) 4s+4m+4L=1000 multiply by 9 (3a) 36s+36m+36l=9000
subtract (3a) from (2)
(2) 30s+36m+48L=9000
(3a) -(36s+36m+36l=9000)
(4) -6s+12l=0 multiply by 4 (4a) -24s+48l=0
multiply (3) by 75 and (1) by 2. & subtract
(3b) 300s+300m+300l=75000
(1a) -( 240s+300m+348l=72000)
(5) 60s-48l=3000
(4a) -24s+48l=0 add
(6) 36s=3000
s=3000/36=250/3
substitute into (4)
-6s+12l=0
-6(250/3)+12l=0
-500+12l=0
12l=500
l=125/3

substitute values for l & s into (3)
(3) 4s+4m+4L=1000
4(250/3) 4m+4(125/3)=1000
1000/3+500/3+4m=3000/3
4m=(3000-1000-500)/3=1500/3=500
m=125

so
s=250/3
m=125
l=125/3

Answer 3

using combination of the second two equations
30s+36m+48L=9000
-36s-36m-36L=-9000

-6s+12L=0
2L=s

Subsitute 2L with s in each equation
207s+150m=36000
54s+36m=9000
6s+4m=1000

combine the first and last equations
207s+150m=36000
-225s-150m=-37500

-18s=-1500
s=250/3 <-

s=2L
L=s/2
L=125/3 <-

subsitute in the last equation
4*250/3+4m+4*125/3=1000
m=125 <-

Answer 4

The first thing you need to do is reduce each equation, then use substitution to solve. When you divide the third equation by 4, you get s + m + L = 250. So s = 250 - m - L. Now, reduce the first and second equations by 6 and then substitute, and you're on your way.

Answer 5

dude i am doing linear equations in math and all but to figure out your problems i would have to see your homework. sorry!