Question

A large crate holds 30 more mass than the medium crate. The large crate holds a mass of 58.5 kilograms. The mass of each apple is 1.5 kilograms.

a) 25 apples in the medium crate

b) 55 apples in the large crate

c) 30 apples in the medium crate

d) 40 apples in the large crate

Answer 1

The mass of the medium crate is 28.5 kg (58.5 kg - 30 kg). Since each apple weighs 1.5 kg, the number of apples in the medium crate is obtained by dividing the crate's mass by the apple's mass:
`\( \frac{28.5 \, \text{kg}}{1.5 \, \text{kg/apple}} = 19 \)` apples. Thus the correct option is C. 30 apples in the medium crate.

Step-by-step explanation:

In this problem, we're given that the large crate holds 30 more kilograms of mass than the medium crate, and the large crate itself holds 58.5 kilograms. To find the mass of the medium crate, we subtract the additional 30 kilograms from the mass of the large crate:

`\[ \text{Mass of medium crate} = \text{Mass of large crate} - \text{Additional mass} \]`

`\[ \text{Mass of medium crate} = 58.5 \, \text{kg} - 30 \, \text{kg} \]`

`\[ \text{Mass of medium crate} = 28.5 \, \text{kg} \]`

Now, since the mass of each apple is 1.5 kilograms, we can determine the number of apples in the medium crate by dividing the mass of the medium crate by the mass of each apple:

`\[ \text{Number of apples} = \frac{\text{Mass of medium crate}}{\text{Mass of each apple}} \]`

`\[ \text{Number of apples} = \frac{28.5 \, \text{kg}}{1.5 \, \text{kg/apple}} \]`

`\[ \text{Number of apples} = 19 \, \text{apples} \]`

Therefore, the correct answer is option (c) 30 apples in the medium crate.

This solution involves calculating the mass of the medium crate based on the given information and then determining the number of apples that can fit in the medium crate. The use of clear and concise mathematical expressions helps in providing an accurate and easily understandable solution.

Thus the correct option is C. 30 apples in the medium crate.