A geometry class has a pizza party. there are 14 students that have a pizza. Each pizza has 8 slices. The teacher wants to buy the least number of pizzas so that they are the same number of slices for each student. (I know the answers, but I don't know how to show the work.)
How many pizzas should be purchased?
How many slices would each student receive?
So, for 14...14,28,56 and
for 8..8,16,24,32,40,32,40,48, 56
Because there is no pizza (or kids for that matter left over) without. 56 is the LCM
56 pieces of pizza must be purchased, so that would be 56slices/8slices per pizza = 7 pizzas.
And, each student would have 56 slices/14 students=4slices/student
(Thank you. I'm Claire's retired grandma. I actually received a scholarship in calculus back in the day....but now can barely remember what a function does!!!)
LOL. I only taught one algebra class, one summer. I enjoyed it tremendously, because the students had failed before and thought they were losers. When they ran to the board to explain their answers, then passed with A's and B's at the summer's end I knew that THEY KNEW they were WINNERS!!!
Find the least common multiple of 14 and 8 to find the total number of pieces. How many pizzas are there?
I'm also a retired teacher -- and a great grandma. But you're ahead of me. My last math class was advanced algebra in high school -- and I almost didn't pass it. <g>
I've learned a lot from Jiskha math tutors.
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I believe any number one chooses (over two) will be the correct number of pizzas to buy; the problem doesn't say there can't be any pieces left over. So anything over 2 pizzas will, in my opinion be right.
2 pizzas will give 16 slices and 16/14 = 1+. So each student gets a single slice and there are 2 slices left over (for the teacher to eat). Or we could buy 3 pizzas and 24/14 = 1+ so each student gets a single slice and there are 10 slices left over for the teacher, etc. So the teacher spends less money on 3 pizzas and gets fat at the same time.
To find the number of pizzas that should be purchased, we need to determine the least common multiple (LCM) of 14 and 8.
The LCM is the smallest number that is a multiple of both 14 and 8. One way to find the LCM is by listing the multiples of each number until we find a common multiple.
For 14, the first few multiples are: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140...
For 8, the first few multiples are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96...
Looking at the lists, we see that the first common multiple of 14 and 8 is 56. So, the LCM of 14 and 8 is 56.
Now, we know that each pizza has 8 slices. To determine how many slices each student would receive, we divide the total number of slices by the number of students:
Total number of slices = Number of pizzas x Slices per pizza
Total number of slices = 56 x 8 = 448 slices
Number of slices per student = Total number of slices / Number of students
Number of slices per student = 448 / 14 = 32 slices
Therefore, the teacher should purchase 56 pizzas, and each student would receive 32 slices.