Fran and Winston have a combined income of $80,000.

Question

One quarter of Winston's income is the same as one-sixth of Fran's income. How much does each person earn? 

Answer 1

Let F = Fran's income

Let W = Winston's income 

 

Combined income is 80000  ==>  F + W = 80000 

 

One quarter of Winston's income is the same as one-sixth of Fran's income  ==>  

 

(1/4)*W = (1/6)*F

 

Multiply the 2nd equation by 12 to clear the fractions  

 

3*W = 2*F

 

Solve this equation for F

 

F = (3/2)*W 

 

Substitute this value for F into the 1st equation 

 

(3/2)*W + W = 80000

(5/2)*W = 80000

W = (2/5)*80000 = 32000

 

So F = 80000 - 32000 = 48000

 

So Winston earns 32000 and Fran earns 48000 

 

Check:  One quarter of Winston's income is 32000/4 = 8000

            One sixth of Fran'e income is 48000/6 = 8000