1. Lisa sold tickets for a local play. Children's tickets cost $4 each and adult tickets cost $6 each. If 383 tickets were sold for a total of $2034, how many of each type of ticket were sold?

132 children's tickets and 251 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of children tickets that were sold.

Let y represent the number of adult tickets that were sold.

A total number of 383 tickets were sold. This means that

x + y = 383

Children's tickets cost $4 each and adult tickets cost $6 each. If the total amount for which the tickets were sold is $2034, it means that

4x + 6y = 2034 - - - - - - - - -- -1

Substituting x = 383 - y into equation 1, it becomes

4(383 - y) + 6y = 2034

1532 - 4y + 6y = 2034

- 4y + 6y = 2034 - 1532

2y = 502

y = 502/2

y = 251

x = 383 - y = 383 - 251

x = 132

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

180

step-by-step explanation: