1) A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. T

Question

1) A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3255 tickets overall. It has sold 203 more $20 tickets than $10 tickets. The total sales are $64,120. How many tickets of each kind were sold?

2) Mike took clothes to the cleaners three times last month. First, he bought 4 shirts and 2 pairs of slacks and paid $16.94. Then he bought 7 shirts, 4 pairs of slacks, and 1 sports coat and paid $38.38. Finally, he bought 4 shirts and 1 sports coat and paid $14.45. How much was he charged for each shirt, pair of slacks, and sports coat?

Explanation / Answer

#(1)

A basketball team sells tickets that cost $10 $20 or VIP seats, $30.

The no. of three types of tickets = x, y, z

The team has sold 3255 tickets over all.

so, x + y + z = 3255............................................(1)

It has sold 203 more $20 tickets than $10 tickets.

so, y = x + 203 ....................................................(2)

The total sales are $64,120.

so, 10x + 20y + 30z = 64120 .........................................(3)

How Many tickets of each kind have been sold?

Replace ( x+ 203) for y in the 1st and 2nd equations

x + ( 203 + x ) + z = 3255

2x + z = 3255 - 203

2x + z = 3052 .......................(4)

and

10x + 20( x + 203 ) + 30z = 64120

10x + 20x + 4060 + 30z = 64120

30x + 30z = 64120 - 4060

30x + 30z = 60060

or,

x + z = 2002 ...................(5)

Now, from the equation (4) and (5), subtracting from (4) , we get:

(2x - x) + ( z - z) = ( 3052 - 2002 )

x = 1050 as $10 tickets sold.

plug in x = 1050 in eqn(2) , we get:

y = 1050 + 203

y = 1253 as $20 tickets sold.

Now, we find z

so, plug in x = 1050 into eqn (4), we get:

2(1050) + z = 3052

2100 + z = 3052

z = 3052 - 2100

z = 952 as $30 tickets sold.

check the solution :

plug in the values of x,y and z into eqn(3), we get:

10(1050) + 20(1253) + 30(952) = 64120

10500 + 25060 + 28560 = 64120

64120 = 64120

Hence, it confirms our solutions.        

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