Twelve of your family members went to the movies. The admission price for adults is $6 and children is $4. How many adults and children went to the movie if the total cost for your family was $54?
X Adults went to movie.
(12-X) Children went.
6x + 4(12-x) = $54.
6x + 48 - 4x = 54
2x = 54 - 48 = 6
X = 3.
12-x = 12-3 = 9.
Let's solve this step by step:
Let's assume the number of adults in your family is A and the number of children is C.
Step 1: Write an equation based on the given information.
The total cost for your family is $54.
So, the equation will be:
6A + 4C = 54
Step 2: Use the fact that there are twelve family members in total.
We know that there are twelve family members in total, so we can write another equation:
A + C = 12
or rearranging, we get:
A = 12 - C
Step 3: Substitute the value of A from equation 2 into equation 1.
Substituting A = 12 - C into equation 1, we get:
6(12 - C) + 4C = 54
Step 4: Simplify the equation.
Expanding the equation, we get:
72 - 6C + 4C = 54
Step 5: Combine like terms and solve for C.
Combining like terms, we get:
72 - 2C = 54
Step 6: Solve for C.
Subtracting 72 from both sides, we get:
-2C = -18
Step 7: Divide by -2 to isolate C.
Dividing both sides by -2, we get:
C = -18 / -2
C = 9
Step 8: Substitute the value of C into equation 2 to find A.
Substituting C = 9 into A = 12 - C, we get:
A = 12 - 9
A = 3
So, there were 3 adults and 9 children who went to the movie.
To solve this problem, let's assume that the number of adults who went to the movies is "A" and the number of children is "C".
We are given the following information:
- The admission price for adults is $6, so we can say that the total cost for adults is 6A.
- The admission price for children is $4, so we can say that the total cost for children is 4C.
- The total cost for the whole family is $54.
Therefore, we can set up an equation based on the given information:
6A + 4C = 54
Now, we need to find the values of A and C that satisfy this equation. Let's try different values of A and C to find the solution that works.
1. Suppose there are 12 adults and 0 children that went to the movies.
- In this case, 6A + 4C = 6(12) + 4(0) = 72 + 0 = 72, which is not equal to 54.
2. Suppose there are 11 adults and 1 child that went to the movies.
- In this case, 6A + 4C = 6(11) + 4(1) = 66 + 4 = 70, which is not equal to 54.
3. Suppose there are 10 adults and 2 children that went to the movies.
- In this case, 6A + 4C = 6(10) + 4(2) = 60 + 8 = 68, which is not equal to 54.
4. Suppose there are 9 adults and 3 children that went to the movies.
- In this case, 6A + 4C = 6(9) + 4(3) = 54 + 12 = 66, which is not equal to 54.
From these calculations, we can see that the number of adults and children must be less than the values we assumed above. Let's try some different combinations.
5. Suppose there are 8 adults and 4 children that went to the movies.
- In this case, 6A + 4C = 6(8) + 4(4) = 48 + 16 = 64, which is not equal to 54.
6. Suppose there are 7 adults and 5 children that went to the movies.
- In this case, 6A + 4C = 6(7) + 4(5) = 42 + 20 = 62, which is not equal to 54.
7. Suppose there are 6 adults and 6 children that went to the movies.
- In this case, 6A + 4C = 6(6) + 4(6) = 36 + 24 = 60, which is not equal to 54.
Based on these calculations, we can conclude that there are no whole numbers of adults and children that satisfy the equation 6A + 4C = 54. Therefore, something might be missing or there might be an error in the given information.