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.

Lets x = # of small tub of popcorn and y = # of large tub of popcorn

She needs to buy at least 7 tubs of popcorn: x + y >= 7

Each small tub of popcorn costs $3 and each large tub of popcorn costs $4 but she only has $24 in her wallet.

3x + 4y <= 24

So now you have the system of inequalities

x + y >= 7

3x + 4y <= 24

Find x and y intercepts of blue line

x + y = 7

x = 0 then y = 7

y = 0 then x = 7

The inequality sign is >= so it's above.

The blue line,  B and D are matching the results

Find x and y intercepts of red line

3x + 4y = 24

x = 0 then 4y = 24; y = 6

y = 0 then 3x = 24;   x = 8

The inequality sign is <= so it's below.

The red line,  Only B is matching

Answer

D is the solution of the system of inequalities.

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75

x=6 and x=3

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