SOLUTION: If the ratio of tourists to locals is 7:8 and there are 210 tourists at the opening of a new museum, how many locals are in attendance?

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Question 1203389: If the ratio of tourists to locals is 7:8
and there are 210
tourists at the opening of a new museum, how many locals are in attendance?

Found 4 solutions by math_tutor2020, ikleyn, MathTherapy, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The ratio of tourists to locals is 7:8

tourists/locals = 7/8
T/L = 7/8
210/L = 7/8
210*8 = L*7
1680 = 7L
7L = 1680
L = 1680/7
L = 240

Answer: There are 240 locals
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

This wording means that there are 7 equal groups of tourists and 8 equal groups of locals of the same cardinality.


From given data, we find the cardinality momentarily: it is   = 30.


So, each group of tourists contains 30 persons, same as each group of locals consists of 30 persons.


As soon as you know it, you get the  ANSWER  in the next instance: the number of locals is 8*30 = 240.

Solved.

Good problem for 3rd grade young students, who are just able to divide and to multiply
integer numbers mentally in their minds.



Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
If the ratio of tourists to locals is 7:8 and there are 210 tourists at the opening of a new museum, how many locals are in attendance?

Let number of locals in attendance be L
Then we get: 

                       
                       7L = 8(210) ----- Cross-multiplying
Number of locals in attendance, or

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


You have already received three responses to your post, showing three different ways to solve the problem. And although the problem is relatively simple, none of those responses shows a common method for solving a problem in which a ratio like 7:8 is given.

Given that the ratio of tourists to locals is 7:8...

let 7x = number of tourists
let 8x = number of locals

That is a common way to start solving a problem in which a ratio is given.

The number of tourists is 210:
7x = 210
x = 210/7 = 30

The number of locals is 8x = 8(30) = 240

ANSWER: 240 locals
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