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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