There are 30 calories in [tex]\frac{1}{4}[/tex] cup of red seedless grapes.

1. How many calories are consumed if a person eats [tex]\frac{3}{4}[/tex] cups of red seedless grapes?

The number of calories in [tex]\frac{3}{4}[/tex] cups of red seedless grapes is [tex]\square[/tex].

2. How many calories are consumed if a person eats [tex]1 \frac{1}{4}[/tex] cups of red seedless grapes?

The number of calories in [tex]1 \frac{1}{4}[/tex] cups of red seedless grapes is [tex]\square[/tex].

3. Write an inequality that represents the number of calories consumed when eating more than [tex]\frac{3}{4}[/tex] but less than [tex]1 \frac{1}{4}[/tex] cups of red seedless grapes.

The inequality is [tex]\square[/tex].



Answer :

Let's solve this problem step-by-step to find the necessary values and understand the inequality that represents the number of calories consumed.

1. Number of calories in [tex]\(\frac{3}{4}\)[/tex] cups of red seedless grapes:

We know that [tex]\(\frac{1}{4}\)[/tex] cup of red seedless grapes contains 30 calories.

To find the calories in [tex]\(\frac{3}{4}\)[/tex] cups, we multiply the calories in [tex]\(\frac{1}{4}\)[/tex] cup by the number of [tex]\(\frac{1}{4}\)[/tex] cups in [tex]\(\frac{3}{4}\)[/tex]:

[tex]\[ \text{Calories in } \frac{3}{4} \text{ cups} = 30 \times 3 = 90 \text{ calories} \][/tex]

2. Number of calories in [tex]\(1 \frac{1}{4}\)[/tex] cups of red seedless grapes:

[tex]\(1 \frac{1}{4}\)[/tex] cups can be rewritten as [tex]\(1 + \frac{1}{4}\)[/tex] cups. Since 1 cup contains 4 quarters and each quarter cup contains 30 calories:

[tex]\[ \text{Calories in } 1 \frac{1}{4} \text{ cups} = \text{Calories in 1 cup} + \text{Calories in } \frac{1}{4} \text{ cup} \][/tex]

Now, calculate the calories separately:

[tex]\[ \text{Calories in 1 cup} = 30 \times 4 = 120 \text{ calories} \][/tex]

[tex]\[ \text{Calories in } \frac{1}{4} \text{ cup} = 30 \text{ calories} \][/tex]

Adding them together:

[tex]\[ \text{Calories in } 1 \frac{1}{4} \text{ cups} = 120 + 30 = 150 \text{ calories} \][/tex]

3. The inequality representing the calories when eating more than [tex]\(\frac{3}{4}\)[/tex] but less than [tex]\(1 \frac{1}{4}\)[/tex] cups:

The range of cup measurements is between [tex]\(\frac{3}{4}\)[/tex] and [tex]\(1 \frac{1}{4}\)[/tex] cups. In calorie terms, this translates to more than 90 calories but less than 150 calories.

Therefore, the inequality can be expressed as:

[tex]\[ 90 \text{ calories} < \text{Calories consumed} < 150 \text{ calories} \][/tex]

In conclusion:

- The number of calories in [tex]\(\frac{3}{4}\)[/tex] cups of red seedless grapes is [tex]\(\boxed{90}\)[/tex].
- The number of calories in [tex]\(1 \frac{1}{4}\)[/tex] cups of red seedless grapes is [tex]\(\boxed{150}\)[/tex].
- The inequality representing the number of calories when eating between [tex]\(\frac{3}{4}\)[/tex] and [tex]\(1 \frac{1}{4}\)[/tex] cups of grapes is [tex]\(\boxed{90 < \text{Calories consumed} < 150}\)[/tex].