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## word problem / fractions

fran and winston have a combined income of \$80000. one quarter of winstons income is equal to one sixth of fans income. how much does each person make?

One quarter of Winston's income is one sixth of Fans income.

This means that Winstons income is 4/6 of Fan's income or 2/3 of Fan's income, so the total income is 1 and 2/3 of Fan's income and is equal to 80000 dollars.

so Fan's income is 80000/(1 and 2/3)  = \$48,000, and Winston's income is 2/3 of that, or \$32,000.

fran and winston have a combined income of \$80000. one quarter of winstons income is equal to one sixth of fans income. how much does each person make?
(1/4)W=(1/6)F
(6/4)W=F
(3/2)W=F
[(3/2)W]+W=80,000
Let's note the fact that W=1w=(2/2)(W)
[(3/2)W]+[(2/2)W]=80,000
Let's combine like terms...
(5/2)(W)=80,000
Let's multiply both sides by 2/5...
(2/5)(5/2)(W)=(80,000)(2/5)
W=32,000
F=80,000-32,000=48,000
Let's check our work...
(1/4)(32,000)=(1/6)(48,000)
8,000=8,000
1) F + W = 80,000
2) F/6 = W/4    (A quarter of Winstons income is equal to one sixth of Frans income)
3) F=3/2W  (rearranging 2)

Plug 3) into 1)

5/2W = 80,000
W = 32,000
F  = 48,000    (Using 3)