Systems of equations

Question

Tickets for the homecoming dance cost $20 for a single ticket or $35 for a couple. Ticket sales totaled $2280, and 128 people attended. How many tickets of each type were sold?

Answer 1

Let S= number of single tickets, C= number of couple tickets.

20S + 35C = 2280

S+2C=128

Multiply the 2nd equation by 20 to get

20S+40C = 2560, then subtract the 1st equation

20S+35C= 2280 to get

5C = 280

C=280/5=56 tickets for couples

S= 128-2C = 128 - 2(56)= 128-112= 16

56 couples tickets, 16 singles tickets were sold

Answer 2

Haiden

Will change your numbers to 30, 50, 2600 and 100.

Suppose x singles, and y couples attend.

Then x + 2y = 100 (1)

Ticket sales 30 x + 50 y = 2600 (2)

We need to find x, y

Multiply (1) by 30

30 x + 60y = 3000

Subtract (2) from this

10y = 400

y = 40

x = 20

Now follow this model, using your numbers

Mike

30 y = 8240

y = 8240 / 30 =