Tickets for a show sold 6 adult tickets and 10 child tickets for a total $96 On the second day12 adult tickets sold and 5 child tickets sold What is the price for adult and child tickets
To find the price of adult and child tickets, we can set up a system of equations based on the information given.
Let's represent the price of an adult ticket as "a" and the price of a child ticket as "c."
From the first day, we know that 6 adult tickets and 10 child tickets were sold, and the total revenue was $96. Using this information, we can write the equation:
6a + 10c = 96 ---(1)
From the second day, we know that 12 adult tickets and 5 child tickets were sold. However, we don't know the total revenue for the second day. Let's refer to it as "R."
Using this information, we can write the equation:
12a + 5c = R ---(2)
Now, we have a system of two equations with two variables. We can solve for "a" and "c" simultaneously.
To solve the system of equations, we can either use substitution or elimination method. Let's use the elimination method to eliminate variable "c."
Multiply equation (1) by 5 and equation (2) by 10 to make the coefficients of "c" equal:
30a + 50c = 480 ---(3)
120a + 50c = 10R ---(4)
Now, subtract equation (3) from equation (4) to eliminate "c":
(120a + 50c) - (30a + 50c) = 10R - 480
90a = 10R - 480
To simplify, we can divide both sides of the equation by 90:
a = (10R - 480) / 90
a = (R - 48) / 9 ---(5)
Now, substitute equation (5) into equation (1) using the values from the first day:
6((R - 48) / 9) + 10c = 96
(R - 48) / 3 + 10c = 96
(R - 48) + 30c = 288
R + 30c = 336
Divide both sides by 30:
c = (336 - R) / 30
c = (56 - R/5) ---(6)
Now, we have the general formulas for "a" from equation (5) and "c" from equation (6). Let's plug in the values from the second day where 12 adult tickets and 5 child tickets were sold:
12a + 5c = R
12a + 5((56 - R/5)) = R
Simplify the equation:
12a + 280 - R = R
12a + 280 = 2R
12a = 2R - 280
6a = R/5 - 140
Now, we can substitute equation (5) into this equation:
6((R - 48) / 9) = R/5 - 140
Simplify further:
2(R - 48) = R/5 - 140
Expand and simplify:
2R - 96 = R/5 - 140
Multiply through by 5 to eliminate the fraction:
10R - 480 = R - 700
Subtract R from both sides and add 480 to both sides:
9R = 220
Divide both sides by 9:
R = 220/9
Now that we have the value of R, we can substitute it back into equation (5) to find "a":
a = (R - 48) / 9
Substituting R = 220/9:
a = 220/9 - 48/9
a = 220/9 - 48/9
a = 172/9
Therefore, the price for adult tickets is $172/9 or approximately $19.11.
Now, we can substitute R = 220/9 into equation (6) to find "c":
c = (56 - R/5)
Substituting R = 220/9:
c = 56 - (220/9)/5
c = 56 - 44/9
c = 500/9
Therefore, the price for child tickets is $500/9 or approximately $55.56.
In summary, the price for adult tickets is approximately $19.11, and the price for child tickets is approximately $55.56.