Mr and Mrs Boyden take their 3 children to a leisure park.
They buy tickets for the whole family.
The cost of an adult ticket is £6 more than the cost of a child ticket.
The total cost of the 5 tickets is £82.
Work out the cost of an adult ticket.
the cost of an adult ticket = 20 if you just want the answer
Let's assume the cost of a child ticket is "x" pounds.
According to the problem, the cost of an adult ticket is £6 more than the cost of a child ticket, so it would be "x + £6" pounds.
Since there are 3 children and 2 adults in the family, the total cost of the 5 tickets is £82.
So we can create an equation to represent this:
3x + 2(x + £6) = £82
Let's solve this equation step by step:
First, distribute the 2 to x and £6:
3x + 2x + 12 = £82
Combine like terms:
5x + 12 = £82
Now, subtract 12 from both sides:
5x = £70
Next, divide both sides by 5:
x = £14
So, the cost of a child ticket is £14.
To find the cost of an adult ticket, we can substitute this value of x back into the equation:
x + £6 = £14 + £6 = £20
Therefore, the cost of an adult ticket is £20.
To work out the cost of an adult ticket, we can set up a system of equations based on the given information.
Let's assume the cost of a child ticket is C. Since the cost of an adult ticket is £6 more than the cost of a child ticket, the cost of an adult ticket would be C + £6.
Now, we can set up the equation to represent the total cost of the tickets. The total cost of the 5 tickets is £82, so we can write the equation as:
3C + 2(C + £6) = £82
Now, we can solve this equation to find the value of C, which represents the cost of a child ticket.
Distribute the 2 to the terms inside the parentheses:
3C + 2C + 12 = £82
Combine like terms:
5C + 12 = £82
Next, subtract 12 from both sides of the equation:
5C = £70
Finally, divide both sides of the equation by 5 to solve for C:
C = £14
So, the cost of a child ticket is £14.
To find the cost of an adult ticket, we can substitute the value of C into our earlier equation:
Adult ticket cost = C + £6 = £14 + £6 = £20
Therefore, the cost of an adult ticket is £20.
ac = cc + 6 so cc = ac - 6
2 ac + 3 cc = 82
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2 ac + 3 (ac-6) = 82
2 ac + 3 ac - 18 = 82
5 ac = 100