Answer:
3 regular-sized boxes and 2 value-pack boxes
6 regular-sized boxes and 2 value-pack boxes
Step-by-step explanation:
Let x = number of regular-sized boxes of forks
Let y = number of value-pack boxes of forks
<u>Inequality 1</u>
Given:
- Regular sized boxes contain enough forks for 16 guests
- Value-pack boxes contain enough forks for 25 guests
- There must be at least enough forks for the 61 guests
<u>Inequality 2</u>
Given:
- Regular sized boxes cost $5 each
- Value-pack boxes cost $10 each
- Maximum money to spend = $60
Therefore, the system of inequalities to describe the scenario is:
To find two solutions that work for the scenario, graph the inequalities.
When <u>graphing inequalities</u>:
< or > : draw a dashed line
≤ or ≥ : draw a solid line
< or ≤ : shade under the line
> or ≥ : shade above the line
Rearrange Inequality 1 to make y the subject:
Rearrange Inequality 2 to make y the subject:
Graph the two lines by drawing a solid line for each.
Shade <u>above the line of first inequality</u> and <u>below the line of the second inequality</u>.
Solutions to the inequalities are any points in the <u>shaded area</u>.
However, solutions to the inequalities for this scenario are any points in the shaded area where <u>x and y are positive integers</u> (see second attached image).
Therefore, two solutions that work for the scenario are:
- 3 regular-sized boxes and 2 value-pack boxes
- 6 regular-sized boxes and 2 value-pack boxes
Learn more about inequalities here:
brainly.com/question/27947009