math help?

Question

1. 1/4y + 2/3y = 12

please show me how you got your answer

i know the answer, but i don't know how to get it. The answer my teacher told me is 144/7

Answer 1

Do you mean 1/(4y) + 2/(3y) = 12
or
do you mean (1/4)y + (2/3)y = 12?

For the first case, you factor out a 1/y, and you have
1/y*(1/4 + 2/3) = 12
Now put the fractions over a common denominator:
1/y*(1/4*3/3 + 2/3*4/4) = 12
1/y*(3/12 + 8/12) = 12
1/y*(11/12) = 12
Now multiply both sides by y:
11/12 = 12y
Divide by 12:
11/144 = y

In the second case, factor out a y and get
y(1/4 + 2/3) = 12
Go through the same steps as before and get
y(11/12) = 12
Divide by 11/12:
y = 12*12/11
y = 144/11

Answer 2

1/4y + 2/3y = 12 multiple every term by 12
3y+8y=144 add like terms
11y=144 divide by 11
y=144/11=13.09

Answer 3

u need to make the 1/4 and the 2/3 have common denominators
by multiplying the 1/4 by 3 and the 2/3 by 4 to get them both over 12
then u can add the fractions to get 11/12y = 12 then multiply the 12 over to get 11y=144

then divide by 11 to y=144/11

Answer 4

12 (1/4y + 2/3y)=(12)12
3y + 8y = 144
11y/11 = 144/11
y = 13.09

Answer 5

Multiply both sides by 12y

3+8=144y

y=11/144

Answer 6

3*4*(1/4y+2/3y)=12*3*4
3y+8y=144
11y=144
y=144/11
y=13.090909090909090909090909090909
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Answer 7

(3+8)/12y=12
11/12y=12
11=12*12y
11/12=12y
y=(11/12)/12=11/144

Answer 8

use the least common denominator which is twelve and combine y, then divide by what will be 11/12ths

Answer 9

11y