Question

1. a small fruit basket contains the fruit shown. a large basket has the same ratio of fruit as the small basket. write and interpret a ratio that compares the number of pears in a small basket to the total pieces of fruit in a small basket. then find the number of pears in a large basket that contains 42 total pieces of fruit. (example 2)

type of fruit	amount
orange	5
pear	3

1. a small batch of trail mix contains 2 cups of raisins, 2 cups of peanuts, 1 cup of sunflower seeds, and 1 cup of candies. a large batch has the same ratio of ingredients as a small batch. write and interpret a ratio that compares the cups of peanuts in a small batch to the cups of sunflower seeds in a small batch. then find the total cups of sunflower seeds in a...

Explanation:

Problem 4

Step1: Calculate total fruit in small basket

First, find the total number of fruits in the small basket by adding the number of apples, oranges, and pears. The number of apples is 6, oranges is 5, and pears is 3. So total fruit $= 6 + 5 + 3 = 14$.

Step2: Find the ratio of pears to total fruit

The number of pears is 3, and total fruit is 14. So the ratio of pears to total fruit is $\frac{3}{14}$. This ratio means that for every 14 pieces of fruit in the small basket, 3 of them are pears.

Step3: Set up proportion for large basket

Let $x$ be the number of pears in the large basket. Since the ratio is the same, we have the proportion $\frac{3}{14}=\frac{x}{42}$.

Step4: Solve the proportion

Cross - multiply: $14x = 3\times42$. Then $14x = 126$. Divide both sides by 14: $x=\frac{126}{14}=9$.

Step1: Identify the amounts

The number of cups of peanuts in a small batch is 2, and the number of cups of sunflower seeds is 1.

Step2: Find the ratio

The ratio of cups of peanuts to cups of sunflower seeds is $\frac{2}{1}=2:1$. This ratio means that for every 1 cup of sunflower seeds in a small batch, there are 2 cups of peanuts.
(Note: Since the problem statement for question 6 seems incomplete (it says "Then find the total cups of sunflower seeds in a..." without finishing), we can only solve the ratio part as above. If we assume we need to find the number of sunflower seeds in a large batch, we would need more information about the total amount in the large batch. But based on the given information, we can at least find the ratio.)

Answer:

The ratio of pears to total fruit in the small basket is $\frac{3}{14}$, meaning 3 out of every 14 fruits in the small basket are pears. The number of pears in the large basket with 42 total fruits is 9.

Problem 6 (assuming we need to solve it as well, since it's a sub - question)