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.
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.
Let's say the number of adults in the group is "A" and the number of students is "S".
We can write two equations based on the given information:
1. A + S = 77 (equation 1) --> There are 77 people in total.
2. 6A + 4S = 338 (equation 2) --> The total ticket cost is $338.
To solve these equations, let's use the method of substitution.
From equation 1, we can rewrite it as A = 77 - S.
Substituting this expression for "A" in equation 2, we get:
6(77 - S) + 4S = 338.
Expanding the expression, we have:
462 - 6S + 4S = 338.
Combining like terms, we get:
-2S = 338 - 462,
-2S = -124.
Dividing both sides by -2, we find:
S = (-124) / (-2),
S = 62.
Now, substitute the value of S back into equation 1 to find the value of A:
A + 62 = 77,
A = 77 - 62,
A = 15.
Therefore, there are 15 adults and 62 students in the group.