431 attended creekview’s musical on Friday night. Admission was $12 each adults and $5.50 each for children. The theatre department made $3183. How many adults and children attended
a = adults
c = childrens
431 attended creekview’s musical on Friday night means:
a + c = 431
Admission was $12 each adults and $5.50 each for children. The theatre department made $3183 means:
12 a + 5.5 c = 3183
Now you must solve system:
a + c = 431
12 a + 5.5 c = 3183
Solution is a = 125 , c = 306
Check results:
a + c = 125 + 306 = 431
12 a + 5.5 c = 12 ∙ 125 + 5.5 ∙ 306 = 1500 + 1683 = 3183
x+y = 431
12x+5.5y = 3183
Multiply Eq1 by 12 and subtract Eq2:
12x+12y = 5172
12x+5.5y = 3183
Diff: 6.5y = 1989
Y = 306 children
x+306 = 431
X = ___ adults.
To find the number of adults and children who attended the musical, we can set up a system of equations based on the information given.
Let's assume the number of adults who attended the musical is represented by the variable 'A', and the number of children is represented by the variable 'C'.
We know that the total number of attendees is 431, so we can write the equation:
A + C = 431
We also know that the total revenue made by the theatre department is $3183, which can be expressed as:
12A + 5.5C = 3183
Now we have a system of two equations with two variables. We can solve this system using various methods, such as substitution or elimination.
Let's use the substitution method. Solve the first equation for A:
A = 431 - C
Substitute this expression for A into the second equation:
12(431 - C) + 5.5C = 3183
Distribute 12 to each term in the parentheses:
5172 - 12C + 5.5C = 3183
Combine like terms:
-6.5C = -1989
Divide both sides of the equation by -6.5 to solve for C:
C = -1989 / -6.5
C ≈ 306
Now substitute this value of C back into the first equation to find A:
A + 306 = 431
A = 431 - 306
A = 125
Therefore, there were 125 adults and 306 children who attended Creekview's musical on Friday night.