Fruit Weight Balance

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Sarah is working at a fruit market. She needs to determine the weights of different types of fruit baskets. The baskets are marked with fruit symbols: an apple, a banana, or a grape. All baskets with the same fruit symbol have the same weight.

The following diagrams show what Sarah observed when arranging some of the baskets and standard weights on a scale.

Determine the weight of each fruit basket.

Fruit Weight Balance Same fruit symbol = same weight. Find the weight of each basket! Clue 1 Clue 2 Clue 3 B A 15 kg B + A = 15 kg A A 6 kg A + A = 6 kg B G G G B = G + G + G Key A Apple basket B Banana basket G Grape basket

Solution

From the diagrams we can observe the following:

  • One banana basket and one apple basket have a total weight of 15 kg.
  • Two apple baskets have a weight of 6 kg.
  • One banana basket has the same total weight as three grape baskets.

Let’s solve this step by step:

  1. Since two apple baskets weigh 6 kg, then the weight of one apple basket is 1/2 of 6 kg. Therefore, one apple basket weighs 3 kg.
  2. We know that one banana basket and one apple basket together weigh 15 kg, and we just found out that one apple basket weighs 3 kg. So, one banana basket must weigh 15 – 3 = 12 kg.
  3. We’re told that one banana basket has the same weight as three grape baskets. Since one banana basket weighs 12 kg, each grape basket must weigh 12 ÷ 3 = 4 kg.

Therefore:

  • One apple basket weighs 3 kg
  • One banana basket weighs 12 kg
  • One grape basket weighs 4 kg
Fruit Weight Balance — Solution Step Result A + A = 6 kg → A = 6 ÷ 2 B + A = 15 → B + 3 = 15 B = 3 × G → 12 = 3 × G A = 3 kg B = 12 kg G = 4 kg Checking all three clues Clue 1: B + A = 12 + 3 = 15 kg ✓ Clue 2: A + A = 3 + 3 = 6 kg ✓ Clue 3: B = G + G + G → 12 = 4 + 4 + 4 = 12 kg ✓ Apple = 3 kg · Banana = 12 kg · Grape = 4 kg