A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?
If a soda costs x, then we have
2hx + sx = 100d
x = 100d/(2h+s)
That was correct, I tried inputting the answer.
To find the cost of a soda, we need to use the information given. Let's break down the problem step by step:
1. Let's start by assigning variables to the given information:
- The number of hot dogs sold: h
- The number of sodas sold: s
- The total amount of money earned: d
2. According to the problem statement, a hot dog costs twice as much as a soda. Let's represent the cost of a soda as x. Therefore, the cost of a hot dog would be 2x.
3. To determine the total earnings, we need to consider the number of hot dogs and sodas sold, along with their respective costs:
- The revenue from hot dogs: h * (2x)
- The revenue from sodas: s * x
4. The total earnings is the sum of the revenues from hot dogs and sodas, so we can write the equation:
d = h * (2x) + s * x
5. Now, let's simplify the equation:
d = 2hx + sx
6. Since we want to find the cost of a soda, we need to isolate the x variable. We can rewrite the equation as:
d = x(2h + s)
7. Divide both sides of the equation by (2h + s) to solve for x:
x = d / (2h + s)
8. Finally, the cost of a soda is represented by x. Since the cost is usually given in dollars, we convert it to cents by multiplying x by 100 to get the answer in cents.
In summary, to find the cost of a soda, divide the total earnings (in cents) by the sum of two times the number of hot dogs plus the number of sodas sold.