
Suzanne O. answered 11/26/19
International Experience and Multiple State Certifications
Hi Ashley. To solve this one:
The Robotics Club was selling food to raise funds for their upcoming trip. They sold a total of 352 hamburgers, cheeseburgers, and hot dogs. The number of cheeseburgers they sold was 6 times the number of hamburgers sold, and they sold 104 more hot dogs than hamburgers. How many hamburgers did they sell? Cheeseburgers? Hot dogs?
You will need to break it into parts.
What we already know:
- They sold a total of 352 hamburgers, cheeseburgers, and hot dogs. In mathspeak, that would read:
- 352 = cheeseburgers + hamburgers + hot dogs
- The number of cheeseburgers they sold was 6 times the number of hamburgers sold. In mathspeak, that would read:
- cheeseburgers = hamburgers x 6
- they sold 104 more hot dogs than hamburgers. Again, translated to mathspeak:
- hot dogs = hamburgers + 104
Now we need to replace some values. Since we have calculated the numbers of cheeseburgers and hot dogs sold as functions of the number of hamburgers sold, we'll use those replacements:
- 352 = cheeseburgers + hamburgers + hot dogs
- 352 = (hamburgers x 6)+ hamburgers + hot dogs
- 352 = (hamburgers x 6)+ hamburgers + (hamburgers + 104)
Now solve the equation:
- 352 = (hamburgers x 6)+ hamburgers + (hamburgers + 104)
- 352 = 8hamburgers + 104
- 248 = 8hamburgers
- 248 ÷ 8 = hamburgers
- hamburgers = 31
Then take hamburgers = 31 back to find the other answers:
- cheeseburgers = hamburgers x 6
- cheeseburgers = 31 x 6
- cheeseburgers = 186
and
- hot dogs = hamburgers + 104
- hot dogs = 31+ 104
- hot dogs = 135
Lastly, check your answers:
- 352 = 31 + 186 + 135
- 352 = 352 ✔