Problem
Rick took his family to a major league football game. He gave his son $100 to buy food and drinks for the group. Hot dogs cost $3.50 each, milkshakes cost $8.00 each, and soda cost $5.00 each. His son returned with $25.50 in change. There were 8 beverages total in the order. Both sodas and milkshakes are considered beverages. How many hot dogs, milkshakes, and sodas were purchased?
Solution
Step 1: Understand the problem
All the relevant components and data that are involved in this problem are:
The total amount was - $100
Hot dogs - $3.50 each
Milkshakes - $8.00 each
Soda - $5.00 each
Change remaining - $25.50
Beverages (sodas+milkshakes) - 8 in number
We are required to find out the individual number of hotdogs, milkshakes and sodas were bought.
Step 2: Devise a plan
The plan to solve this problem will entail forming an equation.
Let; h be the number of hot dogs in the order
m be the number of milkshakes in the order
s be the number of sodas in the order
Out of $100, $25.50 remained, implying that a total of $74.50 was spent. Thus
3.5h + 8m + 5s = 74.5
Given that milkshakes and sodas were 8 in total then,
m + s = 8
Step 3: Carry out the plan
Given that m + s = 8
Then s = 8-m
Thus 3.5h + 8m + 5s = 74.5
3.5h + 8m + 5(8-m) = 74.5
3.5h + 8m + 40 – 5m = 74.5
3.5h + 3m = 34.5
h = 34.5/3.5 - 3m/3.5
Taking this equation of h we will replace with the possible values of m and s to get their values
| m | s | h |
| 0 | 8 | 9.857 |
| 1 | 7 | 9 |
| 2 | 6 | 8.142 |
| 3 | 5 | 7.286 |
| 4 | 4 | 6.429 |
| 5 | 3 | 5.571 |
| 6 | 2 | 4.714 |
| 7 | 1 | 3.857 |
| 8 | 0 | 3 |
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From the table, we see that only the combination 1 milkshakes and 7 sodas or 8 milkshakes and no sodas result to a whole number in the number of hot dogs, which is what is realistic.
This gives two possible answers; 9 hot dogs, 1 milkshake, 7 sodas or
3 hot dogs, 8 milkshakes, 0 soda
Step 4: Check your answer
To check the answer, we replace the values to the original equation
3.5h + 8m + 5s = 74.5
9 Hot dogs, 1 Milkshake, 7 Sodas 3 Hotdogs, 8 Milkshakes, 0 Soda
3.5(9) + 8(1) + 5(7) 3.5(3) + 8(8) + 5(0)
= 74.5 = 74.5
The answers are proved since they both add up to the amount spent which was $74.50.
