Question

At a museum, ticket prices are $13 for adults and $11 for children. If a tour group paid $179 for their tickets, how many people were in the tour group?

Answer 1

7 adults 8 kids

Answer 2

arent there many combinations possible?

Answer 3

(7x13) + (8x11) = 179

Answer 4

that is the ONLY combination?

Answer 5

Well, you can certainly try many possible numbers of adults, from 1 to 14, and see which work.

Answer 6

so no formula?hit and trial?

Answer 7

Diophantine problem. Makes me dizzy. I opened this page.
http://www.wikihow.com/Solve-a-Linear-Diophantine-Equation

Answer 8

13a+11c=179
yup Diophantine equation....

Answer 9

Diophantine equation....:O

Answer 10

http://openstudy.com/users/ParthKohli#/updates/50e43ad3e4b0e36e35145cc6
i have listed 2 different methods here.

Answer 11

one involves modular arithmetic and other involves finding the GCD and its reverse process.

Answer 12

Let A denote the # of adult tickets
Let C denote the # of child tickets

Therefore...

$13 x A + $11 x C = $179
13A + 11C = 179

So from this point forward, I would ask the following. What # must you subtract from $179 in order for it be divisible by 11. That number must also be a factor of 13.

Essentially what I'm saying is 11C = 179-13A

The answer to that would be the following:
13 x 7 = 91
179- 91 = 88
88/11 - 8

Therefore, 7 adults and 8 kids.

PS - You could do it the other way around where you could try to find the number divisible by 179 which is also a factor of 11 but I thought it would be easier to do it the other way around since we're more familiar with our 11 times tables.

from here

http://www.jiskha.com/display.cgi?id=1362991103

Answer 13

No.

Answer 14

?

Answer 15

Just kidding. I meant yes.