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

Answer 1

Taylor and her children bought 4 bags of popcorn and 6 candies.

How to create linear equation using two variables?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation. A specific point on the graph represents the solution of a linear equation in two variables, ax + by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.

Let the number of bags of popcorn be = x
Let the number of candies be = y
Given, she bought $ 81 worth of bags of popcorn and candies.
Also, each bag of popcorn costs $9 and each candy costs $4.50.
Thus, the equation for the same is ⇒ 9x + 4.50y = 81  -- (i)
Again, she bought 6 more candies than bags of popcorn.
Thus, the equation for the same is ⇒ y = x + 6  --(ii)
Using (i) and (ii), we have,
9x + 4.50(x + 6) = 81 ⇒ 9x + 4.50x + 27 = 81 ⇒ 13.50x = 54 ⇒ x = 4
Using x = 4 and (ii), we get,
y = x + 6 = 4 + 6 = 10
Thus, (4, 10) is the point where the two equations meet.
Therefore, they bought 4 bags of popcorn and 6 candies.

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