tnagerine problem

Question

A banana republic held a parliamentary election, and every one of the citizens voted. Everyone who voted for the tangerine party likes tangerines. 90% of the people who voted for one of the other parties don't like tangerines. What percent of the votes did the tangerine party get if 46% of the people like tangerines.

Answer 1

Ok, a problem of ratios, but solved with algebra. P_b = proportion total liking tangerines

P_t = proportion tangerine party liking tangerines P_o = Proportion others liking tangerines

O = others T = Tangerine B = Population of banana republic.

so given O + T = B , P_b = .46 , P_o = .1 and P_t = 1 we can develop a second equation

.1*O + 1*T = .46*B

Solving of two equations for two unknowns is HS algebra. You can use your calculator, do it by hand or use on-line resources. (see below for link)

For a population of 100% (1), the percentage of tangerine trolls (T) = 40% (.40) and the percentage of banana beaters (O) = 60% (.6)

Link

https://www.wolframalpha.com/input?i=systems+of+equations+calculator&assumption=%7B%22F%22%2C+%22SolveSystemOf2EquationsCalculator%22%2C+%22equation1%22%7D+-%3E%22o+%2B+t+-b+%3D+0%22&assumption=%22FSelect%22+-%3E+%7B%7B%22SolveSystemOf2EquationsCalculator%22%7D%7D&assumption=%7B%22F%22%2C+%22SolveSystemOf2EquationsCalculator%22%2C+%22equation2%22%7D+-%3E%22.1+o+%2B+t+-+.46+b+%3D+0%22