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

Sagot :

MrRoyal

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

How to determine the number of 10 tickets?

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

  • x represents the 10 tickets
  • y represents the 15 tickets
  • z represents the 20 tickets

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

Read more about system of equations at:

https://brainly.com/question/14323743

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