Just peanuts
Three kids share 770 peanuts. Every time Alan gets 4 peanuts, Boris gets 3 peanuts, and every time Alan gets 6 peanuts, Carla gets 7 peanuts.
How many peanuts does Alan get?
Problem source: Mattenøtter, Teknisk Ukeblad.
Three kids share 770 peanuts. Every time Alan gets 4 peanuts, Boris gets 3 peanuts, and every time Alan gets 6 peanuts, Carla gets 7 peanuts.
How many peanuts does Alan get?
Problem source: Mattenøtter, Teknisk Ukeblad.
March 11th, 2010 at 5:31 am
A+(3/4•A)+(7/6•A)=770
A•(1+9/12+14/12)=770
A•(35/12)=770
A=770•12/35=264
Alan gets 264.
Boris gets 198.
Carla gets 308.
I’m going to share this with my son. Thanks for the problem!
March 11th, 2010 at 5:43 am
MM:
Many of my students are afraid of fractions, so I rephrased the conditions as “peanut odds” for Alan:Boris:Carla. The odds are 12:9:14, comprising 35 parts in all. Then 770/35 = 22 peanuts per part, and multiplication gives the (same) answer.
Nice problem!
March 11th, 2010 at 10:53 am
MA:
One of the things I love most about math beyond simple arithmetic is that there are often multiple equally correct approaches. Maybe it’s because statistics has never been a strength of mine but that approach leaves me scratching my head. Out of curiosity, with your eye for statistics, do the odds of 12:9:14 just leap out at you without much effort? Maybe it’s time for me to find a statistics course at the local community college.
To whoever it may concern:
Mattenøtter apparently has some gems in it but unfortunately I need a translator. Please feel free to post more of them!
March 11th, 2010 at 12:37 pm
In my class room I have seen that even simple arithmetic can give multiple equally correct approaches.
More problems will come from this Norwegian source (Norwegian is my mother tongue).
Google translated it like this to English:
This task is about three children – John, Peter and Kari – who share a bag of 770 peanuts.
Every time John gets 4 peanuts, get Per 3 peanuts, and every time John gets 6 peanuts, get Kari 7 peanuts.
How many peanuts are Ola?