At the refreshment stand, hotdogs cost 80 cents each lemonades cost 50 cents . A group of students ordered twice as many hotdogs as lemonades. If their bill was $16.80, how many hotdogs are ordered?
number of lemonades ---- x
number of hotdogs ---- 2x
80x + 50(2x) = 1680
take over
To solve this problem, we can follow these steps:
1. Assign variables: Let's denote the number of lemonades as L and the number of hotdogs as H.
2. Translate the information given into equations:
- The cost of a hotdog is 80 cents, so the cost of H hotdogs is 80H cents.
- The cost of a lemonade is 50 cents, so the cost of L lemonades is 50L cents.
- The total bill is $16.80, which is equivalent to 1680 cents.
3. Set up the equations based on the given information:
- The cost equation: 80H + 50L = 1680
- The ratio between hotdogs and lemonades: H = 2L (twice as many hotdogs as lemonades)
4. Solve the system of equations:
- Substitute the value of H from the second equation into the first equation:
80(2L) + 50L = 1680
160L + 50L = 1680
210L = 1680
L = 8
- Now that we know L = 8, we can substitute it back into the second equation to find H:
H = 2L
H = 2(8)
H = 16
5. Answer: The number of hotdogs ordered is 16.