A cinema sells adult tickets and child tickets. The total cost of 3 adults and 1 child is £30 The total cost of 1 adult and 3 children is £22 What is the cost of adult and child tickets
To find the cost of adult and child tickets, let's assign variables to the unknown quantities:
Let's say the cost of an adult ticket = A
And the cost of a child ticket = C
Now, we can use the given information to set up a system of equations.
From the first statement, "The total cost of 3 adults and 1 child is £30," we can write the equation:
3A + 1C = £30
From the second statement, "The total cost of 1 adult and 3 children is £22," we can write the equation:
1A + 3C = £22
Now, we have a system of two equations with two unknowns. We can solve this system using any method we prefer, such as substitution or elimination.
Let's use the elimination method to solve the system:
Multiply the first equation by 3:
(3A + 1C) * 3 = £30 * 3
9A + 3C = £90 (Equation 1)
Next, multiply the second equation by 1:
(1A + 3C) * 1 = £22 * 1
1A + 3C = £22 (Equation 2)
Now, subtract Equation 2 from Equation 1:
(9A + 3C) - (1A + 3C) = £90 - £22
9A - 1A + 3C - 3C = £90 - £22
8A = £68
Divide both sides of the equation by 8:
A = £8.50
Now that we have found the cost of an adult ticket, we can substitute this value back into either of the original equations to find the cost of a child ticket.
Let's use the first equation:
3A + 1C = £30
3 * £8.50 + 1C = £30
£25.50 + 1C = £30
1C = £30 - £25.50
1C = £4.50
Therefore, the cost of an adult ticket is £8.50 and the cost of a child ticket is £4.50.
3a+c = 30
a+3c = 22
take it from there...