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# Part A: if Y and X salary ratio = ¾ Part B: if Y and Z salary ratio = 2/3 And total of salary = 1800\$ The salary of everyone is =?

Part A: if Y and X salary ratio = ¾
Part B: if Y and Z salary ratio = 2/3
And total of salary = 1800\$
The salary of everyone is =?

### 2 Answers by Expert Tutors

Anthony B. | Math, Stats, Calculus, APA TutorMath, Stats, Calculus, APA Tutor
4.8 4.8 (411 lesson ratings) (411)
1
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

Thanks very much
Ira S. | Bilingual math tutor and much moreBilingual math tutor and much more
5.0 5.0 (257 lesson ratings) (257)
0
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
y = 6*1800/23 = \$469.57
z = 9*1800/23 = \$704.35

let's check these since they're such bizarre answers. Remember we rounded these off so it won't come out exact but should be close.
626.09 + 469.57 + 704.35 = 1800.01   pretty close I'd say.
y:x = 3:4 =0.75 our y/x is 469.57/ 626.09  = 0.750003993    pretty close!!!!
y:z = 2:3 = 0.6666666666   OUR y:z is 469.57 / 704.35  = 0.666671399    pretty darn close
So you got some strange answers, but they work!!!!