In a particular tour group, 40% of the tourists are men, and there are 12 more women than men. How many tourists altogether are there in the group? Explain you

Question

In a particular tour group, 40% of the tourists are men, and there are 12 more women than men. How many tourists altogether are there in the group? Explain your reasoning.

Answer 1

The two equations you need in this problem will not come directly from the problem: They will take a little work. The second one is simple ("There are 12 more women than men"):

   W = 12 + M

 

The other equation would normally come from the phrase "40% of the tourists are men". This equation would be VERY useful if we knew the number of tourists. It turns out we can get this indirectly by remembering that the number of men plus the number of women is the number of tourists. Then we have our second equation:

   40/100 * (W + M) = M <-- read "40% of the number of tourists equals the number of men"

 

Substitute the first equation into the second to get:

   40/100 * (12 + M + M) = M

   2/5 * (12 + 2*M) = M

   24/5 + (4/5)*M = M

   24/5 = (1/5)*M

   24 = M

 

Substitute this into the first equation to get:

   W = 12 + 24

   W = 36

 

Now, we answer the question. The number of tourists is 24 + 36 = 60. I hope this helps.

Answer 2

M = # men

W = # women

T = Total # tourists

 

M + W = T  _____ eqn 1

M = .4T ________ eqn 2

W = M + 12 ____  eqn 3

 

Substitute .4T in place of M and

M+12 = .4T + 12 in place of W

in equation 1:

 

.4T + .4T + 12 = T

.8T + 12 = T

12 = T - .8T

12 = .2T

 

T = 12/.2

T = 60 total tourists

 

Check:  M = .4T = 24

        W = M+12 = 36

                          ------

                            60