A local theater charges $8 for adult tickets and $6 for children's tickets to a play. If a group of 24 goes to the theater and pays $164, how many of each ticket type did the group purchase?

The theater was attended by 10 adults and 14 children.

Step-by-step explanation:

As the theater charges adults $ 8 and children $ 6 for each ticket, there is a surcharge of $ 2 for each adult. Thus, given that a group of 24 people attended the theater, as a minimum (that is, if they were all children) the establishment should charge $ 144 (6 x 24). Now, since it charges $ 164, there is a difference of $ 20 (164 - 144), attributable to the surcharge paid by adults for each ticket. Thus, since this surcharge is $ 2, dividing 20 by 2 we obtain 10, which is the number of adults who attended the theater.

This is verified by the following calculation:

10 x 8 = 80

14 x 6 = 84

80 + 84 = 164

Therefore, the theater was attended by 10 adults and 14 children.

your answer would be 12

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it