Meha is helping her aunt to plan a birthday party for her cousin at the science center. He aunt tells her that the party will cost $150, plus $10.50 per child and $5.50 per adult. There needs to be at least one adult and at least one child at the party. She has budgeted $300 for the party and that is the maximum amount she wants to spend. Use the inequality you choose in the last equation. Is it possible for the party to include 10 children and 5 adults? Plug in the number of children (c) and the number of adults (a) into the inequality. You must show all your work to get full points.

Question

GPT-4o mini · Answer

To determine if the party can include 10 children and 5 adults within the budget, we can set up an equation based on the information given.

The total cost of the party can be expressed as:

\[ \text{Total Cost} = 150 + 10.50c + 5.50a \]

where:

$c$ is the number of children
$a$ is the number of adults

Based on the problem, we also need to take into account the budget and set up an inequality:

\[ 150 + 10.50c + 5.50a \leq 300 \]

By plugging the values $c = 10$ (children) and $a = 5$ (adults) into the inequality, we can check if it's satisfied:

\[ 150 + 10.50(10) + 5.50(5) \leq 300 \]

Calculating each component:

$10.50 \times 10 = 105$
$5.50 \times 5 = 27.50$

Now plug those values into the inequality:

\[ 150 + 105 + 27.50 \leq 300 \]

Now add the values together:

\[ 150 + 105 = 255 \] \[ 255 + 27.50 = 282.50 \]

So now we have:

\[ 282.50 \leq 300 \]

Since $282.50$ is less than or equal to $300$, the inequality holds true.

Thus, it is possible for the party to include 10 children and 5 adults within the budget of $300.