Question 233287
A contest winner received one fourth of his winnings in cash, and received four prizes, each worth on fourth of the balance. If the cash and one of the prizes were worth a combined total of 35,000, what was the total value of his winnings?


Let winnings be W


Since he received {{{1/4}}} of his winnings in cash, then he receives {{{(1/4)W}}} in cash. This leaves a remainder of {{{W - (1/4)W}}} or {{{(3/4)W}}}


Now, since the cash he received, plus {{{1/4}}} of the remainder =  35,000


Then we'll have or


{{{(1/4)W + (1/4) * (3/4)W = 35000}}}, or, {{{(1/4)W + (3/16)W = 35000}}}


{{{4W + 3W = 560000}}} -----> Multiply by LCD, 16


{{{7W  =  560000}}}


W = {{{560000/7}}} = $80,000


Therefore, W, or his winnings = ${{{highlight_green(80 000)}}}