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.

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:

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.
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.
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