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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)

Verified Answer :

(10,-5) is the correct naswer

Answer:

(10,1)

Step-by-step 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

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