Algebra 2 help please?

Question

Jims weekly pay is two thirds of Alicias. Together they earn $600 per week. What is each persons weekly pay?

Step by step please im lost with it my teacher said something about the reciprocal(sp) to someone else this is as far as i got to solving it

600=2/3X+X

Answer 1

You're there, go with it...or if you want to see the answer, keep reading...

Let Jim's weekly pay be J and let Alicia's be A, so:
J = 2/3*A
and
J + A = 600

So, substitute for J:
2/3A + A = 600
2/3A + 3/3A = 600
5/3A = 600
5/3A * 3/5 = 600 * 3/5
15/15 * A = 1800/5
A = 360

Since A + J = 600, then
J = 600 - A
J = 600 - 360
J = 240

So, Jim's weekly pay is $240 and Alicia's is $360.

Check the answer:
240 ?= 2/3 * 360
240 = 240 Yes, the answer is correct.

Answer 2

You are correct so far.
Let Alicia's pay = x
Jim's pay will equal 2/3 x
Together the earning are $600
$600 = 2/3x + x
You can write x as 3/3x and then add to 2/3x to get 5/3x
$600 = 5/3x
Now divide both sides by 5/3
$600 / (5/3) = x
When you divide by a fraction, you can multiply by the reciprocal of the fraction (invert and multiply)-
$600 x 3/5 = x
$1800 / 5 = x
x=$360
Alicia makes $360 per week and Jim makes $240.

Answer 3

Alicias pay can be declared X
Jims pay is 2/3s that, so his pay can be decalred (2/3)X
And as you said that must equal 600 dollars.

600 = (2/3)X + X

We must solve for X.

X written by itself is equivalent to writing (1)X (one times X). Because that is just X. 1 can be easily written as a fraction as long as the numerator and denominator are equal. e.g., 1/1, 2/2, 3/3, etc.

You can rewrite the problem to say:

600 = (2/3)X + (3/3)X
If you write it like that you can add the two values together and get:

600 = (5/3)X

You can then multiply both sides by 3, and divide both sides by 5.

X = 360
Which is of course Alicias pay.

Jims is (2/3)X = 240.

Answer 4

2/3X + X = 600
(2x + 3x)/3 = 600
2x + 3x = 1800
5x = 1800
x = 360

So Alicia's pay is $360
& Jim's pay is $240

Answer 5

x = Alicia's pay
2/3x = Jim's
x+2/3x=600
5/3x=600
3/5(5/3)x=600(3/5) [This is where the reciprocals come in]
x=360

Answer 6

j+a=600
j=2a/3
substituting
2a/3+a=600
5a/3=600
a= 360
j= 240