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Question

Ticket prices

Adult: $28

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?

Answer

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

 

 

 

 

1 Reply 1 Like ✔Accepted Answer

Ticket prices
Adult: $28
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 —
adults : 100 units
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.

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