Brain Teasers
What's For Lunch? 2
A man was called forth from his cubicle to perform a time-honored task: get lunch.
His boss, Medster, told him to get a certain number of salads and bagels. A salad costs $1.10, and a bagel costs $1.50. Medster gave him $32.10, the exact amount needed to buy all the items for the 23 people (one item per person). He rushes to The Salad and Bagel Store, and suddenly realizes that he forgot how many bagels and salads to get!
Luckily, the new employee is smart, and successfully figures out how many of each lunch to get.
Using the facts he has, can you figure out how many bagels and salads he needs to get?
His boss, Medster, told him to get a certain number of salads and bagels. A salad costs $1.10, and a bagel costs $1.50. Medster gave him $32.10, the exact amount needed to buy all the items for the 23 people (one item per person). He rushes to The Salad and Bagel Store, and suddenly realizes that he forgot how many bagels and salads to get!
Luckily, the new employee is smart, and successfully figures out how many of each lunch to get.
Using the facts he has, can you figure out how many bagels and salads he needs to get?
Answer
He needs to get 17 bagels, and 6 salads.17 bagels = $25.50
6 salads = $6.60
s = salad
b = bagel
total cost = 32.10
total people = 23
1.1s + 1.5b = 32.10
or
s = (32.10 - 1.5b)/1.1
s + b = 23
or
s = 23 - b
Since both equations equal s, the both equal each other, and can be solved like so:
(32.10 - 1.5b)/1.1 = 23 - b
32.10 - 1.5b = 25.30 - 1.1b
32.10 = 25.30 + 0.4b
6.80 = 0.4b
17 = b
Therefore:
s + 17 = 23
s = 6
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Comments
YAY!!! Congrats Medster! Glad it finally got accepted!
sweet teaser, i tried figuring it out cuz we just did stuff exactly like that in math class but i still didnt get it lol it seems easier in a book
Ahh, that reminds me of 8th grade...Oh, no! Make it stop!!!
I reckon that without a calculator and a sheet of paper, the employee probably wouldn't have used the method given, although he should have got the same result.
I started by figuring what it would cost if everyone wanted a salad, 23*1.1=$25.30.
That leaves 32.1-25.3=$6.80, so clearly some people wanted bagels.
Each bagel costs 1.5-1.1=$0.40 more than the salad, so 6.8/0.4=68/4=17 people wanted the bagel and therefore 23-17=6 wanted the salad.
Imho this is the type of maths/logic that kids should be taught in 8th grade, at least in conjunction with 'algebra' as we know it. "(32.10 - 1.5b)/1.1 = 23 - b" actually condenses the above into one short equation but it's not trivial to solve without pen and paper.
I started by figuring what it would cost if everyone wanted a salad, 23*1.1=$25.30.
That leaves 32.1-25.3=$6.80, so clearly some people wanted bagels.
Each bagel costs 1.5-1.1=$0.40 more than the salad, so 6.8/0.4=68/4=17 people wanted the bagel and therefore 23-17=6 wanted the salad.
Imho this is the type of maths/logic that kids should be taught in 8th grade, at least in conjunction with 'algebra' as we know it. "(32.10 - 1.5b)/1.1 = 23 - b" actually condenses the above into one short equation but it's not trivial to solve without pen and paper.
yeah, I used leftclik's method. it didn't even occur to me to use algebra. eh well. Nice teaser!
Wonderful explanation lefty. I see you are a brilliant product of the Oz education system. KISS!
Since I was doing it without paper, pencil or calculator, I used the same method as leftclick. Like many of the math teasers, algebra is not the best choice, but seems to be most people's default.
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