Question

When comparing fruit weights on a balance scale, Jane notices the following relationships: • 1 orange = 2 bananas • 3 apples = 2 oranges • 1 bunch of grapes = 2 apples Use Jane’s fruit comparisons to determine whether her statements below are true or false. If a statement is false, revise the quantity on the right side of the statement to make it true?

Answer 1

The relationships given by Jane are used to establish the equivalencies between different fruits on a balance scale. Through mathematical proportions, we can confirm that 1 orange equals 2 bananas and subsequently, deduce that 1 bunch of grapes equals 2 bananas for the statements to be true.

Step-by-step explanation:

The question involves using relationships between the weights of different fruits to find equivalencies and validate given statements. Jane's observations on a balance scale indicate that 1 orange equals the weight of 2 bananas, 3 apples equal the weight of 2 oranges, and 1 bunch of grapes equals the weight of 2 apples. Essentially, these are proportions that can be solved mathematically to compare the various fruits.

Let's use these relationships to see if the following statements are true or false:

1. 1 orange = 2 bananas
2. 3 apples = 2 oranges
3. 1 bunch of grapes = 2 apples

From the above relationships, we can deduce the following:

1. Since 1 orange is equal to 2 bananas, the first relationship is true.
2. For the second one, since 3 apples equal 2 oranges, we can substitute the value of an orange (2 bananas) to get:

3 apples = 2 * (2 bananas) = 4 bananas. This implies that 3 apples weigh the same as 4 bananas.

1. The third relationship states that 1 bunch of grapes equals 2 apples. If we refer back to the original relationship where 2 apples = 1 orange = 2 bananas, it follows that the weight of a bunch of grapes is equal to that of 2 bananas. Therefore, the statement should be revised to:

1 bunch of grapes = 2 bananas, to make it true.