word problems

Question

At a concession stand, three hot dogs and two hamburgers cost $8.25'; two hot dogs and three hamburgers cost $8.00. find the cost of one hot dog and the cost of one hamburger

Answer 1

Hi Bianca, let x represent the hot dogs and y represent the hamburgers. We can set up two equations that represent each scenario.

 

Equation 1, cost $8.25:

 

3x + 2y = 8.25

 

Equation 2, cost $8.00:

 

2x + 3y = 8.00

 

Solve for y by eliminating the x variable by multiplying equation 1 by -2 and multiplying equation 2 by 3 and then adding the two equations together.

 

-6x -  4y = -16.50

 6x + 9y =  24.00

--------------------

0x  + 5y =   7.50

 

Divide both sides by 5 gives:

 

y = 1.50, or each hamburger costs $1.50.

 

Substitute for y  in the first equation to solve for x.

 

3x + 3.00 = 8.25

 

Subtract 3.00 from both sides giving:

 

3x = 5.25

 

Divide both sides by 3 giving:

 

x = 1.75, or each hot dog costs $1.75.

 

Solution, hot dogs cost $1.75 and hamburgers cost $1.50.

 

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