TkNeo wrote:If an appliance store sells two sizes of air conditioners, an 8000 BTU air conditioner for $235 and a 14000 BTU air conditioner for $465. If, during a sale, the store sold 3 more of the 8000 BTU models than 14000 BTU models and generated revenue of $3495, how many total air conditioners did it sell.
A: 3
B: 6
C: 9
D: 12
E: 13
I don't have an explanation to the solution but the answer key says C:9
Let's call the # of 8000 models "x" and the number of 14000 models "y".
x = y + 3
and
235x + 465y = 3495
235 (y + 3) + 465y = 3495
235y + 465y + 705 = 3495
700y = 2790
y = not an integer! That's unpossible!
Let's try backsolving.
If we sold 9 machines, then we sold 6 * 8000 and 3 * 14000 (since there were 3 more of the 8000s sold).
Revenue would be:
6(235) + 3(465) = 1410 + 1395 = 2805. Doesn't match the revenue we need, therefore (c) can't be the right answer.
We need more revenue, so let's try more machines.
There's no even number we can sell and generate 3 more 8000s than 14000s, so let's jump right to (e).
If we sold 13 machines, then we sold 8 * 8000 and 5 * 14000.
Revenue would be:
8(235) + 5(465) = 1880 + 2325 > 4000, so now we have too much revenue.
There's no possible integer answer, so it's an impossible question. Where is it from?
