At a club play, 117 tickets were sold. Adults' tickets cost $1.25 and
children's tickets cost $0.75. In all, $129.75 was taken in. How many of
each kind of ticket were sold?
I don't know how to set up the equation.
Work Done
Is it:
1.25x + 0.75y=129.75
this is what I've done but it doesn't seem right!
but you also know that x+y = 117 from which
y = 117-x
now plug that into your first equation and continue.
By process of elimination?
More like substitution.
You already worked out the hard bit:
1.25x + 0.75y = 129.75
and Reiny pointed out that
y = 117-x
So you can replace (substitute) y in your equation:
1.25x + 0.75(117-x) = 129.75
and I'm sure you can see your way home from there.
Ok...I got it now, Thanks
The equation you have set up is correct! Let's break it down to understand why it is the correct equation for this problem.
Let's denote the number of adult tickets sold as 'x' and the number of children's tickets sold as 'y'.
The total income from the adult tickets would be the cost of each adult ticket, which is $1.25, multiplied by the number of adult tickets sold, 'x'. So, the income from the adult tickets can be represented as 1.25x.
Similarly, the total income from the children's tickets would be the cost of each children's ticket, which is $0.75, multiplied by the number of children's tickets sold, 'y'. So, the income from the children's tickets can be represented as 0.75y.
According to the problem, the total income from the tickets sold is $129.75. So, we can set up the equation as follows:
1.25x + 0.75y = 129.75
This equation represents the total income from both types of tickets combined. To find the values of 'x' and 'y', you would need to solve this equation using algebraic methods, such as substitution or elimination.
I hope this explanation helps you to understand how the equation is set up for this problem!