Simon was sent out to buy some fruit, and he came back with 3 bananas and a half-dozen pears. When his mother asked what he had paid, however, the boy wasn’t quite sure.
“I know that each banana cost one cent more than the price of a pear,” he said, “and I noticed that what I paid for the pears was the same as I paid for the bananas but reversed.”
His mother couldn’t quite follow this: “What do you mean by reversed?” she asked him.
“Well, I paid less than a dollar for each little lot,” replied Simon, “and the amounts for the two lots were the same figures, but for one lot they were the other way around.”
This was even more confusing than before. But perhaps you can see how much Simon paid altogether.
We could make a chart and try successive possibilities:
| p | b | 6p | 3b | |
| 1 | 2 | 6 | 6 | |
| 2 | 3 | 12 | 9 | |
| 3 | 4 | 18 | 12 | |
| 4 | 5 | 24 | 15 | |
| 5 | 6 | 30 | 18 | |
| 6 | 7 | 36 | 21 | |
| 7 | 8 | 42 | 24 | ← bingo |
Stella’s student Jasper tried algebra, without result:
pear cost = x, banana cost = x + 1
3 bananas = 3(x + 1) = 3x + 3 = 10t + u
6 pears = 6x = 10u + t
3 bananas = 3(x + 1) = 3x + 3 = 10t + u
6 pears = 6x = 10u + t
| 6x | + | 6 | = | 20t | + | 2u |
| 6x | = | 10u | + | t | ||
| 6 | = | 19t | – | 8u |
So? Can we tease out another equation?