The carnivals arriving in the neighborhood Leo has saved up $15 to spend of the carnival of food and attractions Food items cost $4 each and attractions cost $2 each Leo uses the expression for 4a + 2B to determine the total cost for food items and be attractions What combination of food items and attractions that Leo can afford with is $15 budget

Answer 1

Let's break down the expression you provided: \(4a + 2b\), where:

• \(a\) represents the number of food items Leo buys (costing $4 each),
• \(b\) represents the number of attractions Leo attends (costing $2 each).

Leo has a total of $15 to spend, so we can set up the inequality:

\[ 4a + 2b \leq 15 \]

We can also express it in terms of \(b\):

\[ 2b \leq 15 - 4a \quad \Rightarrow \quad b \leq \frac{15 - 4a}{2} \]

Now, we can find various combinations of \(a\) and \(b\) that satisfy this inequality. Let's explore the possible values of \(a\):

1. If \(a = 0\): \[ 4(0) + 2b \leq 15 \quad \Rightarrow \quad 2b \leq 15 \quad \Rightarrow \quad b \leq 7.5 \] Since \(b\) must be a whole number, \(b\) can be from 0 to 7. (7 options)

2. If \(a = 1\): \[ 4(1) + 2b \leq 15 \quad \Rightarrow \quad 4 + 2b \leq 15 \quad \Rightarrow \quad 2b \leq 11 \quad \Rightarrow \quad b \leq 5.5 \] So, \(b\) can be from 0 to 5. (6 options)

3. If \(a = 2\): \[ 4(2) + 2b \leq 15 \quad \Rightarrow \quad 8 + 2b \leq 15 \quad \Rightarrow \quad 2b \leq 7 \quad \Rightarrow \quad b \leq 3.5 \] So, \(b\) can be from 0 to 3. (4 options)

4. If \(a = 3\): \[ 4(3) + 2b \leq 15 \quad \Rightarrow \quad 12 + 2b \leq 15 \quad \Rightarrow \quad 2b \leq 3 \quad \Rightarrow \quad b \leq 1.5 \] So, \(b\) can be from 0 to 1. (2 options)

5. If \(a = 4\): \[ 4(4) + 2b \leq 15 \quad \Rightarrow \quad 16 + 2b \leq 15 \] This means \(b\) must be negative, which is not possible, so this case does not work.

Now let's summarize viable combinations of \(a\) and \(b\):

• For \(a = 0\): \(b = 0\) to \(7\) (8 combinations)
• For \(a = 1\): \(b = 0\) to \(5\) (6 combinations)
• For \(a = 2\): \(b = 0\) to \(3\) (4 combinations)
• For \(a = 3\): \(b = 0\) to \(1\) (2 combinations)

Summary of Combinations:

1. \((0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7)\)
2. \((1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5)\)
3. \((2, 0), (2, 1), (2, 2), (2, 3)\)
4. \((3, 0), (3, 1)\)

Therefore, Leo can afford a variety of combinations of food items and attractions with his $15 budget, ranging from all attractions to a mix of food and attractions.