#
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.