Question

Taylor and her children went into a movie theater and she bought $81 worth of bags of popcorn and candies. Each bag of popcorn costs $9 and each candy costs $4.50. She bought 6 more candies than bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn,

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,
x, and the number of candies,
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,
y, that Taylor bought.

Answer 1

Answer: (x = 3, y = 9)

Explanation:

We can set up a system of equations to represent the given information. Let x be the number of bags of popcorn, and y be the number of candies. Then we have:

9x + 4.5y = 81 (the total cost is $81)

y = x + 6 (she bought 6 more candies than bags of popcorn)

To graphically solve this system of equations, we can plot both equations on the same graph and look for the point of intersection.

To graph the first equation, we can rearrange it to slope-intercept form:

4.5y = -9x + 81

y = (-2)x + 18

To graph the second equation, we can rearrange it to slope-intercept form:

y = x + 6

Now we can plot both lines on the same graph:

(May be difficult to see on phone) ->>>>

y

|

12 -| . (3,9)

11 -| .

10 -| .

9 -| .

8 -|

7 -|

6 -| .

5 -| .

4 -| .

3 -| .

2 -| .

1 -| .

0 -|_______________________

0 1 2 3 4 5 6 7 8 x

The point of intersection is (3,9), which means that Taylor bought 3 bags of popcorn and 9 candies.