Trip to the museum
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?
The answer is 15.
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12 solutions
My solution goes like this, assuming x to be the number of adults and y to be number of children, then 1 3 x + 1 1 y = 1 7 9 then, y = 1 1 1 7 9 − 1 3 x ⟹ x ≡ 1 3 1 7 3 m o d 1 1 ⟹ x ≡ 1 3 3 6 m o d 1 1 . Since 4 ≡ 1 6 9 m o d 1 1 we multiply both to get 4 x ≡ 1 3 3 6 . 1 6 9 m o d 1 1 ≡ 1 1 7 m o d 1 1 , which on further simplifying gives x ≡ 7 m o d 1 1 → e q u a t i o n 1 . From the question it is clear that x < 1 6 , therefore either x = 7 o r 1 8 , since x = 1 8 , therefore x = 7 . Sustituting in y = 1 1 1 7 9 − 1 3 x we get y = 8
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he dude what's up are u going 2 write the next epic in the form of mathematics
there is a mistake in your statement that you said there are "x" number of adults and 11 number of children but instead of 11 there will be "y" number of children,
i think u solved by guessing
divide 179 by 13 until the reminder is divisible by 11. i.e. 179 divided by thirteen gives quotient 7 and reminder 88. dividing 88 by 11 gives quotient 8. so 7 + 8 = 15
Moderator note:
It's not clear to me what is meant by "divide 179 by 13 until the remainder is divisible by 11". If I divide 179 by 13, I get 13 reminder 10, since 1 7 9 = 1 3 × 1 3 + 1 0 .
I think it is subtract...
179-13=166(1) 166-13=153(2) 153-13=140(3) 140-13=127(4)
127-13=114(5) 114-13=101(6) 101-13=88(7) which is divisible by 11.
@Challenge Master u can read my solution.
13 adults n 1 child
13 x 7 = 91 179- 91 = 88 88/11 - 8
Therefore, 7 adults and 8 kids.
13*11=143, 179-143=33 and 33/3=3 so, there can also be 11 adults and 3 kids?
How do you know there are 7 adults and 8 kids there without guessing it?
let no. of adults be x and no. of children be y, so equation becomes 13x + 11y = 179,since x and y are integers 11y= 179 - 13x by putting x=1,2,3... =179-13=166(not a multiple of 11) 179-13 2 = 153(not a multiple of 11) similarly.. we get 179-13 7=88(multiple of 11) hence no. of adults=7 and no. children= 8 total=7+8= 15
The nearest odd-number to 179 that is higher is 195 and a multiple of 13. Since a child pays 2 less each $2 is one less person. Hence, 195-179 gives 16, divide that by two to get the number of children giving you 8 children and 7 adults adding up to 179. 8 children plus 7 adults is 15 people
Moderator note:
I understand your idea, though it could be expressed clearer. The first line should be written as
The smallest odd multiple of 13 which is higher than 179 is 195.
The idea here, is that if C is the number of children and A is the number of adults, then we have that 1 1 C + 1 3 A = 1 7 9 . We know that 1 3 ( C + A ) = 1 7 9 + 2 C is a multiple of 13 that is larger than 179, and also odd. If 1 3 ( C + A ) = 1 9 5 , then we get that 2 C = 1 9 5 − 1 7 9 = 1 6 which gives C = 8 .
If 1 3 ( C + A ) ≥ 2 2 1 , then 2 C ≥ 4 2 and C ≥ 2 1 , but then the cost of their tickets would be 1 1 C ≥ 2 3 1 > 1 7 9 , hence it's not possible.
let "a" be the number of adults and "b" be the number of children and cost for adults(a) is 13 and cost for children(b) is 11, so like this total cost for adults is 13a and total cost for children is 11b then according to the question thier sum is 179, mathematically 13a+11b = 179 and like this we found that if a=7 and b=8 then by putting their values in the above equation we get 179 on left side which would be equal to right hand side.
let the no of adult be A and no of children be C then Ax13 + Cx11 = 179 Ax(11+2) + Cx11 = 179 11x(A+C) + 2xA = 179 breaking 179 such that the first part is a multiple of 11 and the second part is an even no (because A can't be fraction value)
11x(A+C) + 2xA = 165 + 14 (where 165 = 11x15) 11x(A+C) + 2xA = 11x15 + 2x7 comparing both sides we get A+C=15 ie the total no of people in the tour group.
Try subtracting 13, until you get to a multiple of 11.
13x7=91 179-91=88 88/11=8 7+8=15
13x+11y=179 solve for non-negative integral solutions of x & y.
simple
multiply 13 with 7=91
179-91=88
88/11=8
7+8=15
VOTE IT UP
How do u get 7 adults
If participants all are adults then 179=13N. but 179 not divisible by 13. 179=13.13+10. that means some children participate too.guess 13n+11m=179 then 11m=10+13(N-n).least value of (N-n) for this is 6 so 13(7)+11(8)=179. Guess there exist an other solution l>m so that 13p+11l=179 here p<n. that means 13(n-p)=11(l-m) which means that we are thinking about lcm of 13 & 11. since 11,13 prime so least number for this solution is 11.13=143. so l=21 & p= -4. hence p is negative then n=7 m=8 is only solution for this problem.
We can write the problem in this equation: 13x + 11y = 179 where x is the number of adults and 11 is the number of children We rewrite the equation to 11y = 179 - 13x 179 - 13x must be divisible to 11 so we try numbers that will make it divisible to 11 we try 7 = 179 - 13 (7) = 179 - 91 = 88 now we have 11y = 88 so y = 8 then we substitute y = 8 to the original equation 13x + 11 (8) = 179 and we'll get that x = 7 To get the total people in the tour group, we get x + y which is 7 + 8 = 15 So there are 15 people in the tour group