Question

Two

thousand

tickets

were

sold

for

entry

to

the

Heritage

Village

,

generating

$

19

,

700

.

The

prices

of

the

tickets

were

$

5

for

children

,

$

10

for

local

adults

,

and

$

12

for

foreign

adults

.

There

were

100

more

tickets

foreign

adults

sold

than

for

local

adult

s

a

.

Derive

a

system

of

three

equations

showing

the

information

given

.

b

.

Use

퐂퐫퐚퐦퐞퐫

′

퐬

퐑퐮퐥퐞

to

find

the

number

of

each

type

of

tick

Answer 1

Total number of tickets sold = 2000

Let number of tickets sold to children be "x"

Let number of tickets sold to Local Adults be "y"

Let number of tickets sold to Foreign Adults be "z"

Since the total number of tickets sold = 2000

x + y+ z = 2000 (1)

Total Revenue genrated by selling tickets = $19,700.

Revenue Generated by selling Children Tickets = number of tickets * price of each ticket

= x * 5 = 5x

Revenue Generated by selling Local AdultsTickets = number of tickets * price of each ticket

= y * 10 = 10y

Revenue Generated by selling Foreign Adults Tickets = number of tickets * price of each ticket

= xz* 12 = 12z

Total revenue = 19700

5x + 10y +12 z = 19700 (2)

Since there were 100 more tickets foreign adults sold than for local adult

Number of localTickets sold + 100 = number of foriegn tickets sold

y +100 = z (3)

So we have got 3 equations now we can find the solution by solving these equations

Substituting value of "z" from eq (3) in eq (1) we get

x + y + ( y+100 ) = 2000

x + 2y +100 = 2000

x +2y = 1900 (4)

Substituting value of "z" from eq(3) in eq(2) we get

5x + 10y +12 (y +100) = 19700

5x + 10y +12y +1200 =19700 // distributing "12" over the bracket

5x + 22y = 18500 (5)

Multiplying eq (4) by "-5" and adding to eq(5) we get

5x + 22y = 18500

-5x -10y = -9500 // multiplied eq(4) by "-5"

12y = 9000

y = 750

from eq (3)

z = y +100

z = 850

from eq(1)

x + y+z =2000

750 +850 +x = 2000

x = 400

Children tickets sold = 400

Local Adults tickets sold = 750

Foreign Adults tickets sold = 850