Admission to a museum is $10 for each adult and $5 for each child. If a group oh 30 people pays a total of $175 in admission how many adults are in the group?
let x = number of adults
let y = number of children
There are 30 people in the group, so x+y = 30
The total cost is $175, so 10x + 5y = 175
10x + 5y = 175
Divide by 5:
2x + y = 35
Now subtract the two equations:
2x + y = 35
x + y = 30
x = 5
Substitute x into one of the equations to find y.
5 + y = 30
y = 25
Now plug both values into the other equation to check your work.
2(5) + 25 = 35
10 + 25 = 35
35 = 35
Your answers are correct.
To solve this problem, we need to set up a system of equations based on the information given. Let's assume the number of adults in the group is 'A' and the number of children is 'C.'
From the given information, we know that the admission for each adult is $10, so the total admission cost for adults is 10A. Similarly, the admission for each child is $5, so the total admission cost for children is 5C.
We are also given that the total admission cost paid by the group is $175. So our first equation is:
10A + 5C = 175
The second equation is based on the total number of people in the group, A + C = 30.
Now we have a system of equations:
10A + 5C = 175
A + C = 30
To solve this system of equations, we can use the substitution or elimination method. In this case, let's use the substitution method. Solve the second equation for A, which gives us A = 30 - C.
Now substitute this value of A in the first equation:
10(30 - C) + 5C = 175
Simplify the equation:
300 - 10C + 5C = 175
-5C = 175 - 300
-5C = -125
Divide both sides of the equation by -5 to isolate C:
C = -125 / -5
C = 25
Now substitute the value of C back into the second equation to find A:
A + 25 = 30
A = 30 - 25
A = 5
Therefore, there are 5 adults in the group.