Question

Kendra and Tom are hosting a dinner party. They have $10 to spend on salad ingredients. The grocery store has lettuce for $2.25 per head and tomatoes for $2.65 per pound.

Using x to represent the number of heads of lettuce and y to represent the number of pounds of tomatoes, Kendra and Tom write the following inequalities.

Kendra: 2.25x+2.65y<10


Tom: 2.25x+2.65y>10

Are both correct, or is one of them incorrect?

Answer 1

Here are 4 scenarios. Determine which can be purchasable and which cannot.
2 heads of lettuce and 1 pound of tomatoes
1 head of lettuce and 3 pounds of tomatoes
2 heads of lettuce and 2 pounds of tomatoes
3 heads of lettuce and no tomatoes

Answer 2

To determine whose inequality is correct, we need to understand the context of their spending for salad ingredients.

Kendra states the inequality as:
\[ 2.25x + 2.65y < 10 \]
This means that the total cost of the salad ingredients (lettuce and tomatoes) must be less than $10, which is a valid condition since they cannot exceed their budget.

Tom states the inequality as:
\[ 2.25x + 2.65y > 10 \]
This implies that they would spend more than $10 on the ingredients, which contradicts their budget of $10.

Since Kendra's inequality accurately reflects their budget constraint (total spending must be less than or equal to $10), and Tom's inequality inaccurately suggests they would exceed their budget, we can conclude that Kendra is correct and Tom is incorrect.

Answer 3

To determine whether each scenario is purchasable within the budget of $10, we can calculate the total cost using the prices given:

- The cost of each head of lettuce is $2.25.
- The cost of each pound of tomatoes is $2.65.

Now, let's calculate the total cost for each scenario:

1. **2 heads of lettuce and 1 pound of tomatoes:**
\[
\text{Total cost} = (2 \times 2.25) + (1 \times 2.65) = 4.50 + 2.65 = 7.15
\]
*This is less than $10; therefore, it is purchasable.*

2. **1 head of lettuce and 3 pounds of tomatoes:**
\[
\text{Total cost} = (1 \times 2.25) + (3 \times 2.65) = 2.25 + 7.95 = 10.20
\]
*This exceeds $10; therefore, it is not purchasable.*

3. **2 heads of lettuce and 2 pounds of tomatoes:**
\[
\text{Total cost} = (2 \times 2.25) + (2 \times 2.65) = 4.50 + 5.30 = 9.80
\]
*This is less than $10; therefore, it is purchasable.*

4. **3 heads of lettuce and no tomatoes:**
\[
\text{Total cost} = (3 \times 2.25) + (0 \times 2.65) = 6.75 + 0 = 6.75
\]
*This is less than $10; therefore, it is purchasable.*

### Summary:
- **Purchasable:**
- 2 heads of lettuce and 1 pound of tomatoes
- 2 heads of lettuce and 2 pounds of tomatoes
- 3 heads of lettuce and no tomatoes

- **Not Purchasable:**
- 1 head of lettuce and 3 pounds of tomatoes