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. a. Define the variables b. Write a system of inequality c. Give 2 possible solutions

Answer 1

3 burgers and 2 Nachos or

2 burgers and 4 Nachos.

Explanation:

a.)Define variables;

Let n represent Nachos

and b represent burgers

b. System of inequality;

2n+4b ≤ 16

n+b ≥ 5

c. Give 2 possible solutions;

First, using the inequalities above, solve for n;

n ≥ 5-b, then replace n with (5-b) in the second equation;

2(5-b)+4b ≤ 16

10-2b+4b ≤ 16

2b ≤ 16-10

2b ≤ 6

b ≤ 3

Using 3 for b, solve for n;

n+3 ≥ 5

n ≥ 5-3

n ≥ 2

Therefore, one possible solution is ; 3 burgers and 2 Nachos

The second solution can be found this way;

If b=2 use equation 2n+4b ≤ 16 to solve for n;

2n+(2*4) = 16

2n+8= 16

2n=16-8

2n=8

n=4

Therefore second solution is 2 burgers and 4 Nachos.