Simultaneous equations-
The tickets for a sports club disco cost £2 for members and £3 for non-members.
a)The total ticket money collected was £580.
x tickets were sold to members and y tickets were sold to non-members.
Use this information to write down an equation involving x and y.
b) 250 people bought tickets for the disco.
Write down an other equation involving x and y.
(a) 2x+3y = 580
Now you try (b)
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a) To write down an equation involving x and y, we need to consider the total ticket money collected. From the information given, we know that tickets for members cost £2 and tickets for non-members cost £3.
Let's break down the equation step-by-step using the given information:
1. x tickets were sold to members, so the total amount collected from members is 2x pounds (£2 per ticket multiplied by x tickets).
2. y tickets were sold to non-members, so the total amount collected from non-members is 3y pounds (£3 per ticket multiplied by y tickets).
According to the problem, the total ticket money collected was £580. Thus, we can write down the equation:
2x + 3y = 580
b) To write down another equation involving x and y, we need to consider the total number of people who bought tickets for the disco. The problem states that 250 people bought tickets.
Since each person can only purchase one ticket, the total number of tickets sold will be equal to the total number of people who bought the tickets (250). Therefore, the equation can be written as:
x + y = 250
So, the two equations involving x and y are:
1. 2x + 3y = 580
2. x + y = 250