Question

Christopher buys 120 hot dog buns for a picnic. He buys two different brands of hot dog buns. Brand X has 12 hot dog buns in a package that costs $4.50. Brand Y has 8 hot dog buns in a package that costs $3.50. Christopher spends $49.50 on hot dog buns. a. Write a system of equations that can be used to find the number of packages of Brand X hot dog buns, x, and Brand Y hot dog buns, y, that Christopher buys. b. Solve the system of equations to find the values of x and y. Show your work or explain how you know.

Answer 1

A system of equations that can be used to find the number of packages of Brand X hot dog buns and Brand Y hot dog buns that Christopher buys is:

12x + 8y = 120  

4.5x + 3.5y = 49.50.

The number of packages of Brand X bought is 4 and the number of packages of Brand Y bought is 9

The following equations can be derived from the question

12x + 8y = 120  equation 1

4.5x + 3.5y = 49.50 equation 2

x represents the number of packages of Brand X

y represents the number of packages of Brand Y

The elimination method would be used to determine the values of x and y

Multiply equation 1 by 4.5 and equation 2 by 12

54x + 36y = 540 equation 3

54x + 42y = 594 equation 4

 Subtract equation 3 from 4

6y = 54  

Divide both sides of the equation by 6

y = 9

Substitute for y in equation 1

12x + 8(9) = 120

12x + 72 = 120

12x = 48

x = 4

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