A survey of a group of tourists was taken in St. Louis. The survey showed the following: of the tourists plan to visit Gateway Arch; plan to visit the zoo; plan to visit the Art Museum and the zoo, but not the gateway Arch; plan to visit the Art Museum and the Gateway Arch, but not the zoo; plan to visit the Gateway Arch and the zoo, but not the Art Museum; plan to visit the Art Museum, the zoo, and the Gateway Arch; plan to visit none of the three places. How many plan to visit the Art Museum only?

14 people visited art museum.

Step-by-step explanation:

A Group of 115 tourists took in St. Louis.

61 tourists plan to visit the Gateway,

48 plan to visit the zoo,

11 plan to visit the Art Museum  but not the Gateway arch,

12 plan to visit the Art Museum, but not the zoo,

17 plan to visit the Gateway arch and zoo but not the art museum,

Seven plan to visit the art museum, the zoo and gateway arch,

Sixteen plan to visit none of three places.

How many plans to visit the art museum?

Let

Number of tourists plan to visit Art museum = x

People plan to visit none of three places = 16 = 115 – 16 = 99

People who visited gateway arch = 61 - 12 - 17 -7=  25

People who visited zoo = 48 – 11 – 17 – 7 = 13

People who visited art museum = 99 – 11 – 17- 7 – 25 – 13 = 14

14 people visited art museum.

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15