A group of 77 people, consisting of students and adults, are going to a museum. An adult ticket costs $6 and a student ticket cost $4. The groups total ticket cost is $338.

Answer 1

Let's use the variables "a" and "s" to represent the number of adults and students in the group, respectively. We can set up two equations based on the information given:

a + s = 77 (because the group consists of 77 people in total)
6a + 4s = 338 (because the total ticket cost is $338)

Now we can use substitution or elimination to solve for one of the variables. Let's use substitution and solve for "a":

a = 77 - s (from the first equation, solving for "a")
6(77 - s) + 4s = 338 (substituting this expression for "a" in the second equation)
462 - 6s + 4s = 338 (distributing the 6)
462 - 2s = 338 (combining like terms)
-2s = -124 (subtracting 338 from both sides)
s = 62 (dividing both sides by -2)

So there are 62 students in the group. We can use the first equation to find the number of adults:

a + 62 = 77 (substituting 62 for "s" and solving for "a")
a = 15

Therefore, there are 15 adults in the group. We can check our work by plugging these values into the second equation:

6(15) + 4(62) = 90 + 248 = 338

So the solution is: there are 15 adults and 62 students in the group.