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Can someone help me with this

Can someone help me with this-example-1

1 Answer

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Answer:

  • corn dogs: $1.25
  • fries: $3.50

Explanation:

You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.

Setup

The cost of each purchase can be represented by the equations ...

  • 2d +3f = 13
  • 4d +f = 8.50

Solution

Subtracting the second equation from twice the first gives ...

2(2d +3f) -(4d +f) = 2(13) -(8.50)

5f = 17.50 . . . . . . simplify

f = 3.50 . . . . . . . divide by 5

4d = 8.50 -f = 5.00 . . . . use the second equation to find d

d = 1.25 . . . . . . divide by 4

Corn dogs cost $1.25; chili-cheese fries cost $3.50.

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Additional comments

Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.

The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.

Can someone help me with this-example-1
User Sunil Verma
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