Question

The band is selling snacks during lunch.Nachos are 2$ each and burgers are $4 each.You want to buy at least 5 items.You want to spend no more than $16 total.
Define the variables
Write a system of inequality
Give 2 possible solutions

Answer 1

For this case we have:

x: Let the variable representing the number of nachos

y: Let the variable representing the number of hamburgers

If you want to buy at least 5 items we have:

$x + y \geq5$

If you cannot spend more than $16 we have:

$2x + 4y \leq16$

Thus, the inequality system is given by:

$x + y \geq5\\2x + 4y \leq16$

Possible solutions:

Now we have to buy 3 nachos and 2 hamburgers:

$3 + 2 \geq5\\5 \geq5$

Is fulfilled!

$2 (3) +4 (2) \leq16\\6 + 8 \leq16\\14 \leq16$

Thus, you can buy 3 nachos and 2 hamburgers.

If you buy 2 nachos and 3 hamburgers:

$2 + 3 \geq5\\5 \geq5$

Is fulfilled!

$2 (2) +4 (3)\leq16\\4 + 12 \leq16\\16 \leq16$

Is fulfilled!

Thus, you can buy 2 nachos and 3 hamburgers.

ANswer:

$x + y \geq5\\2x + 4y \leq16$

You can buy 3 nachos and 2 hamburgers.

You can buy 2 nachos and 3 hamburgers.