Algebra 2-inequalities

Question

Anna is buying pizzas and wings for a party. Large one-item pizzas cost $9.00 each. A bucket of wings costs $12.00. She has $55.00 to spend. Write an inequality to represent the cost of her food for the party. Anna also knows she will by two pizzas. Write an inequality to represent this. Identify 2 solutions that will work for Anna. 

Answer 1

It says that Anna knows she will buy two pizzas

which are $9.00 each.  Letting W = # wing buckets;

 

2(9.00) + 12W ≤ 55.00

18.00 + 12W ≤ 55.00

12W ≤ 55.00 - 18.00

12W ≤ 37.00

W ≤ 37.00/12

W ≤ 3 1/12

 

After buying the two pizzas Anna has a little more

than the cost of 3 buckets of wings.  Since she is not

going to buy 1/12 of a bucket of wings then the

inequality representing the number of wing buckets is

 

W ≤ 3

 

Lets check.  If Anna buys two pizzas and 3 buckets

of wings she spends:

2(9) + 3(12) = 18 + 36 = $54.00

 

She has $1 left over. More if she buys less than 3

buckets of wings.

Answer 2

Hi Lindsay,

 

It looks like for the first part of this question your teacher is asking you to create an equation using inequalities. Once you get the first part, you should be able to figure out the second on your own.

Lets call the number of pizzas Anna buys as X and the number of buckets of wings she buys as Y. So we know that the total amount of food she will by is X+Y. We also know the prices of pizza and wings, so we can say that the total price of the food she will buy is

 

$9.00X + $12.00Y.

 

Because we have been given Anna's spending limit, we know that the total price of food she can buy will have to be less than or equal to $55.00.

 

So let's put all that together. The total price of food (represented by $9.00X + $12.00Y) has to be less than or equal to (≤) $55.00

 

That inequality will look like: $9.00X + $12.00Y ≤ $55.00.

 

With that inequality, you should be able to figure out the second part of the problem!