# Question

Ticket prices

Child: \$16

On Saturday, 300 more children than adults attended the performance. On Sunday, the number of children decreased by 40% while the number of adults increased by 20%. The concert hall with a capacity of 2700 seats was only 70% full on Sunday. What was the total amount of money collected from the sales of child tickets on both days?

This is a Simultaneous Equation.

 S1 S2 S1 × 6 S2 × 5 S1 + S2 Child 100 60 600 300 900 Adult -100 120 -600 600 0 Number 300 1890 1800 9450 11250

2700 × 0.7 = 1890

900u = 11250

1u = 11250 ÷ 900 = 12.5

160u = 160 × 12.5 = 2000 children

2000 × \$16 = \$32000

100u = 12.5 × 100 = 1250 children

1250 – 300 = 950 adult

100a =950

1a = 950 ÷ 100 = 9.5

220a = 9.5 × 220 = 2090 adults

2090 x \$28 = \$58520

58520 + 32000 = \$90520

Ticket prices
Child: \$16

On Saturday, 300 more children than adults attended the performance. On Sunday, the number of children decreased by 40% while the number of adults increased by 20%. The concert hall with a capacity of 2700 seats was only 70% full on Sunday. What was the total amount of money collected from the sales of child tickets on both days?

“This is a Simultaneous Equation.

2700 × 0.7 = 1890
900u = 11250
1u = 11250 ÷ 900 = 12.5
160u = 160 × 12.5 = 2000 children
2000 × \$16 = \$32000

100u = 12.5 × 100 = 1250 children
1250 – 300 = 950 adult
100a =950
1a = 950 ÷ 100 = 9.5
220a = 9.5 × 220 = 2090 adults
2090 x \$28 = \$58520

58520 + 32000 = \$90520″

The question posed is : “What was the total amount of money collected from the sales of child tickets on both days?”

0 Replies 0 Likes

Saturday —
children : 100 units + 300

Sunday —
adults : 100 units x (100% + 20%) = 120 units
children : 100 units + 300 x (100% – 40%) = 60 units + 180

2700 x 70% = 1890 (seats filled on Sunday)
120 units + 60 units + 180 = 180 units + 180 = 1890
1 unit = (1890 – 180)/180 = 9.5
100 units + 300 + 60 units + 180 = 160 units + 480 = 160 x 9.5 + 480 = 2000
2000 x 16 = 32000

Ans : \$32000.

0 Replies 0 Likes