Alegebra Help ASAP

Question

The Miller family visited Mama's Kitchen and ordered 4 hamburgers and 3 medium fries and paid $17.13. James ordered a medium drink, a hamburger, and 2 medium fries and paid $8.07. Steven ordered 2 hamburgers, medium fries, and a medium drink for $8.94. How much did each item cost?

Answer 1

First, lets define a few variables:

 

d = Medium Drink

f = Medium Fry

h = Hamburger

 

Now, lets convert each of these statements into an equation:

 

#1 The Miller family visited Mama's Kitchen and ordered 4 hamburgers and 3 medium fries and paid $17.13

So, we get the equation 4h + 3f = 17.13.

 

#2 James ordered a medium drink, a hamburger, and 2 medium fries and paid $8.07

From this, we get the equation d + h + 2f = 8.07

 

#3 Steven ordered 2 hamburgers, medium fries, and a medium drink for $8.94

Finally, this gets us the equation 2h + f + d = 8.94

 

The first equation is the only one of the three to only consist of two variables -- so we can isolate one of the variables and solve.

 

So we take the first equation 4h + 3f = 17.13 and we will solve for h.

 

4h + 3f = 17.13

4h = 17.13 - 3f

Divide both sides by 4:

h = 4.2825 - .75f

 

Now that we have solved for h we can substitute this into the other two equations.  Substituting in h in the first equation we get:

 

d + 4.2825 - .75f + 2f = 8.07

Simplify:

d + 1.25f = 3.7875

 

 

Substituting in h in the second equation we get:

2(4.2825 - .75f) + f + d = 8.94

Simplify:

8.565 - 1.5f + f + d = 8.94

-.5f + d = .375

 

So now we have a normal set of two equations with two variables.  We can use simple substitution to solve for the variables.  Let's solve for d first.  Using the first equation, we can subtract 1.25f from both sides to get:

 

d = 3.7875 - 1.25f

 

Substitute this in the second equation for d and get:

 

-.5f + 3.7875 - 1.25f = .375

Simplify and solve:

3.4125 - 1.75f = 0

3.4125 = 1.75f

f = 1.95

 

Now we have the price of one of the variables (fries).  Lets punch this into the equation for d and we can solve for d:

 

d = 3.7875 - 1.25(1.95)

d = 3.7875 - 2.4375

d = 1.35

 

Now we have another variable (drink).  The final variable to solve for is the hamburger and we can use any of the original equations to solve for it.  Lets take the very first one:

 

4h + 3f = 17.13

Substitute in f:

4h + 3(1.95) = 17.13

4h + 5.85 = 17.13

4h = 11.28

h = 2.82

 

That's the last variable.  So the hamburgers are $2.82, the fries are $1.95, and the drinks are $1.35.

 

I hope that helped!

Answer 2

Let h = price of hamburger

Let f = price of medium fries

Let d = price of medium drink

 

1)  Miller family:  4h + 3f = 17.13

2)  James:            h + d + 2f = 8.07

3)  Steven:         2h + d + f = 8.94

 

We can eliminate d by subtracting equation 2 from equation 3

 

3)   2h + d + f = 8.94

2) -(h + d + 2f = 8.07)

     -------------------------

      h + 0d -f = .87

4)   h - f = .87

We can use this equation along with equation 1 to find h and f

 

4)    h - f = .87

1)  4h+3f = 17.13

 

Multiply equation 4 by 3 and add to equation 1

 

3h - 3f = 2.61       3(equation 4)

4h + 3f = 17.13    equation 1

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

7h + 0f = 19.74

7h = 19.74

h = 19.74/7

h = $2.82

 

hamburgers cost $2.82

 

We know h-f = .87 so..

2.82 - f = .87     subtract 2.82 from both sides

-f = .87 - 2.82

-f = -1.95

f = 1.95

 

medium fries cost $1.95

 

h + d + 2f = 8.07

2.82 + d + 2(1.95) = 8.07

d + 2.82 + 3.90 = 8.07

d + 6.72 = 8.07

d = 8.07 - 6.72

d = 1.35

 

medium drinks cost $1.35