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 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.