Question

Iced tea, x, costs $4 per gallon and lemonade, y, costs $6 per gallon. You need to purchase at least 9 gallons of drinks for a neighborhood picnic, but have at most $55 to spend. Model the scenario with a system of inequalities. Which of the following options represents a possible solution to the system of inequalities?

(10,10)
(10, -5)
(2,10)
(10,1)

(It is not 10,-5 so just don't copy the old answers)

Answer 1

D is our choice

Explanation:

For the money part we get

4x+6y ≤55

For the gallons we get

x+y ≥9

I will use elimination so multiply the second equation by -4

Remember when multiplying by a negative, the inequality flips

-4x -4y ≤-36

Add the first equation and the last equation together to eliminate x

4x+6y ≤55

-4x -4y ≤-36

----------------------

2y ≤19

Divide by 2

2y/2 ≤19/2

y ≤9.5

Now we need to find x

x+y ≥9

Substitute y in

x+9.5 ≥9

Subtract 9.5 from each side

x+9.5-9.5 ≥9-9.5

x ≥-.5

Also 4x+6y ≤55

Let y=0

4x ≤55

Divide by 4

4x/4 ≤55/4

x ≤13.76

Two things

We cannot buy parts of a gallon so y ≤9, x<13

and x and y cannot be negative ( no selling drinks we are buying them) so x ≥0 ,y ≤0

0 ≤y≤9

0 ≤x≤13

Which points fits these requirements

A and C have y >9 so they are eliminated

B has y as negative so it is eliminated

D is our choice