May Answer:Problem: It's lunch time at Powerhouse Secondary School, and the students are hungry again for ________________ (please fill in a type of Keebler snack). Yesterday, the Powerhouse students, 7th - 12th graders, ate 360 snacks during lunch. The 7th graders ate 1.5 times as much as the 9th graders. The 11th graders snacked on 1/4 of the number that the 7th graders ate. The 10th graders devoured as many as the 11th graders and 8th graders combined. The 12th graders ate ten fewer snacks than the 11th graders. Not to be outdone by the 12th graders, the 8th graders ate 1/3 as many as the 7th graders. How many snacks were eaten by each class?
Solution: An ideal strategy for this problem is guess & check (trial & error). Students need to determine which grade level is the easiest to build on. From there, students can choose numbers, match the clues, and see if they meet the criteria of 360 total snacks. If not, students should analyze their total, increasing/decreasing their original guesses to come closer to the snack total.
What is Known:
Total snacks = 360
7th = 1.5 x 9th grade
8th = 1/3 of 7th grade
9th =
10th = 11th & 8th
11th = 1/4 of 7th grade
12th = 11th -10 snacks
*A good place to begin guessing: 7th grade & 9th grade
Example:
If 9th is 69, 7th is 1.5x60 or 90
So, 8th is 1/3 of 7th, or 30
11th is 1/4 of 7th, or 1/4x90=90/4=22.5
10th is 11th+8th, 30+22.5= 52.5
12th is 10 less than 11th(22.5) = 12.5
Final Answer:
7th = 120 snacks
8th = 40 snacks
9th = 80 snacks
10th = 70 snacks
11th = 30 snacks
12th = 20 snacks