# Problem of the Week Problem C and Solution Berry Picking

## Problem

Owen, Gabriel, and Ariane work as strawberry pickers at a local farm. One week Owen picked $$135$$ more strawberries than Gabriel, and Ariane picked $$110$$ more strawberries than Owen. In total that week Owen, Gabriel, and Ariane picked $$2000$$ strawberries.

Determine the number of strawberries that each person picked.

## Solution

Solution 1

Let $$g$$ be the number of strawberries that Gabriel picked. It follows that Owen picked $$(g+135)$$ strawberries and Ariane picked $$(g+135+110)$$ strawberries. Since they picked $$2000$$ strawberries in total, we can write and solve the following equation: \begin{aligned} g + (g +135) + (g + 135 + 110) &= 2000\\ g + (g + 135) + (g + 245) &= 2000\\ 3g + 380 &= 2000\\ 3g &= 1620\\ g &= 540 \end{aligned} So, $$g+135 = 675$$ and $$g+135+110 = 785$$.

Thus, Gabriel picked $$540$$ strawberries, Owen picked $$675$$ strawberries, and Ariane picked $$785$$ strawberries.

Solution 2

If Owen had picked $$135$$ fewer strawberries, and Ariane had picked $$135+110=245$$ fewer strawberries, then each would have picked the same number of strawberries as Gabriel. In that case, each person would have picked $$\frac{1}{3}$$ of $$(2000-135-245)$$, which is $$\frac{1}{3} \times 1620=540$$ strawberries.

Thus, Gabriel picked $$540$$ strawberries. Then Owen picked $$540+135=675$$ strawberries and Ariane picked $$540+245=785$$ strawberries.