Question

Your family likes to go to baseball games. At one game your family bought 5 soft drinks and 5 hot dogs for $22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for $14.50. What is the cost of one soft drink and one hot dog? Let s = the cost of one soft drink Let h = the cost of one hot dog a. Write a system of equations modeling the situation described above. b. Solve the system for the cost of one soft drink + one hot dog. (You will have to add your solutions together for this one.)

Answer 1

Explanation:

The first equation is

5s + 5h = 22.25

The second equation is

4s + 3h = 14.50

If we solve this system by elimination, we can multiply the first equation by -4 and the second one by +5 to first eliminate the s terms. After multipying each equation through by its scalar multiple, we have a new set of equations:

-20s - 20h = -89

20s + 15h = 72.50

Now the s terms subtract each other away, leaving us with

-5h = -16.5 so

h = 3.30

Now we can take that h value and sub it back into one of the original equations and find s:

5s + 5(3.3) = 22.25 and

5s + 16.5 = 22.25 and

5s = 5.75 so

s = 1.15

For one drink and one hot dog you will spend 1.15 + 3.30 = $4.45

Answer 2

$4.45

Explanation:

(a) The situation can be modeled by the system of equations ...

5s + 5h = 22.25

4s +3h = 14.50

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(b) You are asked to find the value of s+h. Divide the first equation by 5 and you have that result:

s + h = 4.45

The cost of one soft drink and one hot dog is $4.45.

_____

Comment on the problem and solution

The first step in solving the problem is to understand how what you're given relates to what you're asked to find.

Here, you're given a value for 5 drinks and 5 hot dogs, and you're asked to find the value of 1 drink and 1 hot dog. You do not need to know the individual costs of the items. The cost of 1 combination is 1/5 the cost of 5 of them.