Question

Dahlia is preparing meals for a holiday party. She is providing two options for each person attending: vegan meals or non-vegan meals. each vegan meal cost three dollars, and each non-vegan meal costs $4.50. there will be at least 20 people attending the party, and dahlia can spend at most $100 for preparing the meals. Write a system of equations representing the scenario.

Answer 1

Answer:

a)

A system of equations representing the scenario is;

$\begin{gathered} x+y\ge20\text{ ---------1} \\ 3x+4.50y\le100\text{ ---------2} \end{gathered}$

b)

she meets both requirements If she prepared 15 vegan and 10 non-vegan meals. because the total number of meals is at least 20 and the cost is less than $100.

Explanation:

Given that each vegan meal cost $3.00, and each non-vegan meal cost $4.50.

Let x represent the number of vegan meals and y represent the number of non-vegan meals.

And there will be at least 20 people attending the party;

$x+y\ge20\text{ ---------1}$

Also, dahlia can spend at most $100 for preparing the meals;

$3x+4.50y\le100\text{ ---------2}$

Therefore, a system of equations representing the scenario is;

$\begin{gathered} x+y\ge20\text{ ---------1} \\ 3x+4.50y\le100\text{ ---------2} \end{gathered}$

If she prepares 15 vegan and 10 non-vegan meals

We need to confirm if it meets both conditions;

condition 1;

$\begin{gathered} x+y\ge20\text{ ---------1} \\ 15+10\ge20 \\ 25\ge20 \\ \text{condition satisfied} \end{gathered}$

Condition 2;

$\begin{gathered} 3x+4.50y\le100\text{ ---------2} \\ 3(15)+4.50(10)\le100\text{ ---------2} \\ 45+45\le100 \\ 90\le100 \\ \text{Condition satisfied} \end{gathered}$

Therefore, she meets both requirements If she prepared 15 vegan and 10 non-vegan meals. because the total number of meals is at least 20 and the cost is less than $100.