a concert promoter sold 475 tickets to a rock concert the ticket prices for different seat locations were 10 15 and 20 the total

Question

2 years ago

14

income from the concert was 6300 if the combined number of 10 15 tickets sold was 4 times the number of 20 tickets sold how many 10 tickets were sold

1 answer:

Andrej [43] · Answer 1 · 2023-08-25T14:55:09+03:00

282.5 of 10 tickets were sold in the rock concert by the promoter

<h3>How to determine the number of 10 tickets?</h3>

To do this, we make use of the following representations:

The 475 tickets that were sold means that:

x + y + z = 475

The income means that:

10x + 15y + 20z = 6300

Also, we have:

10y = 4z

Divide both sides by 10

y = 0.4z

Substitute y = 0.4z in 10x + 15y + 20z = 6300

10x + 15*0.4z + 20z = 6300

10x + 6z + 20z = 6300

Evaluate the like terms

10x + 26z = 6300

Substitute y = 0.4z in x + y + z = 475

x + 0.4z + z = 475

Evaluate the like terms

x + 1.4z = 475

Make x the subject

x = 475 - 1.4z

Substitute x = 475 - 1.4z in 10x + 26z = 6300

10(475 - 1.4z) + 26z = 6300

Expand

4750 - 14z + 26z = 6400

Evaluate the like terms

12z = 1650

Divide both sides by 12

z = 137.5

Substitute z = 137.5 in x = 475 - 1.4z

x = 475 - 1.4 * 137.5

Evaluate

x = 282.5

Hence, 282.5 of 10 tickets were sold

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