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.

Question

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

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 2

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 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