The carnival is arriving in the neighborhood! Leo has saved up $15 to spend at the carnival on food and attractions. Food items cost $4 each and attractions cost $2 each. Leo uses the expression 4a + 2b to determine the total cost for a food items and b attractions.

Question

Select one of the following combinations of food items and attractions that Leo can afford with his $15 budget:

(1 point)
Responses

1 food item and 5 attractions
1 food item and 5 attractions

0 food items and 8 attractions
0 food items and 8 attractions

2 food items and 4 attractions
2 food items and 4 attractions

3 food items and 2 attractions
3 food items and 2 attractions

Answer 1

To determine which combination Leo can afford with his $15 budget using the expression \(4a + 2b\), let's evaluate each option:

1. 1 food item and 5 attractions:
   \[ \text{Cost} = 4(1) + 2(5) = 4 + 10 = 14 \] This is within the budget of $15.

2. 0 food items and 8 attractions:
   \[ \text{Cost} = 4(0) + 2(8) = 0 + 16 = 16 \] This exceeds the budget of $15.

3. 2 food items and 4 attractions:
   \[ \text{Cost} = 4(2) + 2(4) = 8 + 8 = 16 \] This also exceeds the budget of $15.

4. 3 food items and 2 attractions:
   \[ \text{Cost} = 4(3) + 2(2) = 12 + 4 = 16 \] This exceeds the budget of $15 as well.

The only combination that Leo can afford is 1 food item and 5 attractions.