At a football game, a dad purchases hot dogs for $1.25 and drinks for $1.75. If he purchases 9 items for $13.25, how many of each did he purchase?

Question

At a football game, a dad purchases hot dogs for $1.25 and drinks for $1.75. If he purchases 9 items for $13.25, how many of each did he purchase?

Answer 1

Let's say that the dad bought H (hot dogs) and D (drinks). Those are our variables.

 

We are told that he bought 9 items, so 

 

H + D = 9

 

Now let's establish the total cost. If the hotdogs are 1.25 each and the drinks are 1.75 each, we can sum the cost of those to get a total.

 

1.25(H) + 1.75(D) = 13.25

 

Now, we have two equations and two variables (unknowns), which is awesome because we can now solve this "system" of equations.

 

We can get "H" by itself in the first equation by subtracting D to get:

 

H = 9 - D

 

Now "substitute" this into the second equation

 

1.25 * (9 - D) + 1.75 * D = 13.25                   distribute the 1.25

 

11.25 - 1.25D + 1.75D = 13.25                       combine like terms (the Ds)

 

11.25 + 0.5D = 13.25                                    subtract 11.25 from each side

 

0.5D = 2                                                        divide by 0.5 (or multiply by 2, whichever is easier for you)

 

D = 4

 

Recall that D is the variable for drinks. The dad bought 9 items, which means that he bought 5 hot dogs.

 

You can easily check this solution by multiplying the cost of each item by the number of items purchased.

 

1.75(4) + 1.25(5) = 13.25

 

I hope this helps!

Answer 2

Let h = the number of hot dogs and d = the number of drinks.

 

h + d = 9

1.25h + 1.75d = 13.25

 

First, let's solve the first equation for either d or h. I'll do d.

 

d = 9 - h

 

Next, I'm going to substitute 9 - h into the 2nd equation for d, since they are equal...

 

1.25h + 1.75(9 - h) = 13.25

1.25h + 15.75 - 1.75h = 13.25

-.50h = -2.50

h = 5

 

d = 9 - h = 9 - 5 = 4

 

5 hot dogs and 4 drinks were purchased.

 

Hope this helps!

Answer 3

Dogs cost $1.25,  Drinks cost $1.75, Purchased 9 items for $13.25

 

Let D = number hot dogs;   9 - D = number of drinks bought

 

        $1.25D + $1.75 ( 9 - D ) = $13.25

 

Multiply all three terms by 100 to get rid of decimals

 

              125D + 175 ( 9 - D ) = 1325

 

             125D + 1575 - 175D = 1325

 

                        - 50D + 1575 = 1325

 

                                     -50D = -250

 

        D = 5 hot dogs;  9 - 5 = 4 drinks

 

This problem could be worked using two equations

 

 

Answer 4

H = number of hot dogs at 1.25 each

 

D = number of drinks at 1.75 each

 

(i)   H + D = 9

 

(ii)  1.25H + 1.75D = 13.25

 

Just solve the 2 equations above in 2 unknowns H and D:

 

From (i), H = 9 - D.  Plug this into (ii) and get

 

1.25(9 - D) + 1.75D = 13.25

 

D = 4

 

Then H = 9 - 4 = 5

 

He purchased 5 hot dogs and 4 drinks.