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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 =?

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2 Answers

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
 

Comments

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!!!!

Comments