Question

A container of mixed nuts contains 75 ounces of peanuts , almonds , and walnuts only . The ratio of the weights of peanuts and almonds is 5:7 , and the ratio of the weights of almonds to walnuts is 7:3. If all the peanuts were removed , what would be the new weight of the container ? A. 40 oz. B. 50 oz. C. 60 oz. D. 70 oz

Answer 1

Explanation:

To solve this problem, we need to determine the weights of almonds and walnuts, as well as the combined weight of almonds and walnuts.

Let's assume the weight of peanuts is 5x ounces.

Then, the weight of almonds is 7x ounces.

Furthermore, the weight of walnuts is 3/7 * 7x = 3x ounces.

The combined weight of almonds and walnuts is 7x + 3x = 10x ounces.

Since the weight of peanuts is 5x ounces, the total weight of the container is 5x + 7x + 3x = 15x ounces.

If all the peanuts were removed, the new weight of the container would be 10x ounces.

However, we don't have the value of x, so we can't determine the exact weight in ounces.

Therefore, the correct answer cannot be determined without additional information.

The options A, B, C, or D are not valid choices.

Answer 2

B. 50 oz.

Explanation:

Given that the ratio of the weights of peanuts and almonds is 5:7, and the ratio of the weights of almonds to walnuts is 7:3, we can find the common ratio by combining these ratios.

The combined ratio of peanuts, almonds, and walnuts is 5:7:3.

Let's represent the weights of peanuts, almonds, and walnuts as 5x, 7x, and 3x, respectively.

The total weight of the mixture is given as 75 ounces:

`\tt 5x + 7x + 3x = 75`

`\tt 15x = 75`

`\tt x = (75)/(15)`

`\tt x = 5`

Now that we have the value of x, we can determine the weight of almonds and walnuts:

Weight of almonds
`\tt = 7x = 7 * 5 = 35` ounces

Weight of walnuts
`\tt = 3x = 3 * 5 = 15` ounces

Weight of peanuts
`\tt = 5x = 5*5 = 25` ounces

In order to find the new weight of the container after removing all the peanuts, we add the weights of almonds and walnuts:

New weight of the container = Weight of almonds + Weight of walnuts

New weight of the container = 35 + 15

New weight of the container = 50 ounces

Therefore, the new weight of the container after removing all the peanuts would be 50 ounces.

The correct answer is B. 50 oz.