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)

Answer 1

(10,-5) is the correct naswer

Answer 2

(10,1)

Explanation:

Let No. of iced tea be x

Let no. of lemonades be y

We are given that You need to purchase at least 9 gallons of drinks

So, equation becomes:
`x+y\geq 9` --1

Cost of 1 gallon of ice tea = $4

Cost of x gallons of ice tea = $4x

Cost of 1 gallon of lemonade = $6

Cost of y gallons of lemonade = $6y

We are also given that you have at most $55 to spend.

So, equation becomes:
`4x+6y\leq 55` ---2

Now Check the given points which satisfies the inequalities

`x+y\geq 9` and
`4x+6y\leq 55`

At (10,10)

`10+10\geq 9` and
`4(10)+6(10)\leq 55`

`20\geq 9` and
`100\leq 55`

(10,10) is not satisfying the both equations

At (10,-5)

`10-5\geq 9` and
`4(10)+6(-5)\leq 55`

`5\geq 9` and
`10\leq 55`

(10,-5) is not satisfying the both equations

At (2,10)

`2+10\geq 9` and
`4(2)+6(10)\leq 55`

`12\geq 9` and
`68\leq 55`

(2,10) is not satisfying the both equations.

At (10,1)

`10+1\geq 9` and
`4(10)+6(1)\leq 55`

`11\geq 9` and
`46\leq 55`

(10,1) is satisfying the both equations.

Thus (10,1) is a possible solution to the system of inequalities