The question is: in a car dealership, there are sedans,convertibles, and both. 1/3 of sedans are convertibles and1/5 of convertibles are sedans. What could be the possiblenumber of total cars in the dealership?Please explain this problem with a clear diagram and clear stepsthat justify the final solution.Thanks.

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Dante Patton · Accepted Answer

Let T be the total number of carsLet S be the number of sedansLet C be the number of convertablesLet G be the number of convertable sedansThe problem states:1/3 of sedans are convertables and 1/5 of convertables aresedans and the dealership has only sedans, convertables, andconvertable sedans.T = S + C + G (1)1/3   ×S = G (2)1/5   ×C = G (3)equating the equations (2) and (3) we have1/3   ×S = 1/5   ×CS = 3/5   ×C (4)now substituting equations (3) and (4) into equation (1) wehaveT = 3/5   ×C + C + 1/5   ×CT = 9/5   × C (5)Since there can only be a whole number of cars we have toeliminate the fractions in equation (5) and check to make surethere are a whole number of sedans, convertibles, and convertablesedans.Let there be 5 convertiblesfrom (5)T = 9/5   × 5 = 9 total carsfrom (4)S = 3/5   × 5 = 3 sedansfrom (3)G = 1/5   × 5 = 1 convertable sedanBecause the question was worded, &quot;What could be a possible numberof total cars in the dealership&quot; we could have gotten anyfactor of 9.In other words there is a possible 9n total cars, where nis any positive integer.

In a car dealership, there are sedans,convertibles, and both. 1/3 of sedans are convertibles and1/5 of convertibles are sedans. What could be the possiblenumber of total cars in the dealership?

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