Part B: if Y and Z salary ratio = 2/3

And total of salary = 1800$

The salary of everyone is =?

Part B: if Y and Z salary ratio = 2/3

And total of salary = 1800$

The salary of everyone is =?

Tutors, sign in to answer this question.

Hello Karim,

First off, when we are given a ratio, we can turn it into an equation with opposite coefficients. So we have:

4y=3x

3y=2z

Total salary means that we add all three salaries:

x+y+z=1800

We now have a system of three equations and three variables, so we can solve it now. We start by solving the first equation for x.

4y=3x

x=4/3y

And solve the second equation for z,

3y=2z

z=3/2y

We can plug both of these into the third equation now.

x+y+z=1800

4/3y+y+3/2y=1800

Change to common denominator 6 and add.

8/6y+6/6y+9/6y=1800

23/6y=1800

y=1800*6/23

y=$469.57

Now we can plug this into the first two equations and solve there also.

4y=3x

4(469.57)=3x

1878.26=3x

x=$626.09

3y=2z

3(469.57)=2z

1408.71=2z

z=$704.36

y:x = 3:4 can be reversed to say x:y = 4:3. y:z = 2:3. If we make the y terms into the same number, in this case 6, we can create what's called an extended ratio. So

x:y = 8:6 and y:z = 6:9 so the ratio of x:y:z = 8:6:9 . Using the ratio factor method, that is if we multiply each number by the same factor, the numbers change but the ratio stays the same, we can write 8r +6r+9r = 1800. So 23r =1800 and r=1800/3. Not a very nice number!!!! But we'll go with it. Plug it back into the ratio then round to nearest hundredth since we're dealing with money.

x = 8*1800/23 = $626.09

thanks very much

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