Question

Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn costs $4. She needs to buy at least 7 tubs of popcorn, but she only has $24 in her wallet.
If the solution region represents the number of small and large tubs of popcorn that Katie can buy, determine which graph represents the solution set to the system of inequalities representing this situation.

Answer 1

Answer:

Option 1

Step-by-step explanation:

Let  x be the no. of small tub popcorn.

Let y be the number of large tub popcorn.

She needs to buy at least 7 tubs of popcorn

So, equation becomes : $x+y\geq 7$ --1

Cost of 1 small tub of popcorn = $3

Cost of x small tub of popcorn = $3x

Cost of 1 large tub of popcorn = $4

Cost of y large tub of popcorn = $4y

Now we are also given that she only has $24 in her wallet.

So, equation becomes : $3x+4y\leq 24$  --2

Now

$x+y\geq 7$   ---blue line in the given graphs

At(0,0)

$0+0\geq 7$ False .

So, region bounded by this line is away from origin

$3x+4y\leq 24$   -- red line in the given graphs

At(0,0)

$3(0)+4(0)\leq 24$

$0+0\leq 24$ True

So, region bounded by this line is towards origin

So, in the given graphs Option 1 Satisfies the obtained conditions.

So Option 1 is true.

Answer 2

The first graph. 

The blue line represents the minimum number of popcorn tubs you must buy. That needs to be shaded above. 

The red line represents the amount of money that you have to spend. That must be shaded below.