Do NowThe owner of a movie theater was counting the money from

1 day’s ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7.50 each and children’s tickets cost $4.75 each. If the total receipts for the day were $891.25, how many of each kind of ticket were sold?

Homework Solutions11) Let s = hourly cost of sprayer

Let g = hourly cost of generator

6s + 6g = 90 12s + 12g = 1804s + 8g = 100 – 12s + 24g = 300

– 12g = – 120 g = 10

6s + 6g = 906s + 6(10) = 906s + 60 = 906s = 30 s = 5

The sprayer cost $5 / hour and the generator $10 / hour.

Homework Solutions12) Let r = number of robins

Let c = number of cardinals

r = 3cr + c = 20

3c + c = 20 4c = 20

c = 5 r = 3cr = 3(5)r = 15

5 cardinals and 15 robins

Homework Solutions13) Let g = number of grasshoppers

Let c = number of crickets

g + c = 561g = 2c

2c + c = 561 3c = 561

c = 187 g = 2cg = 2(187)g = 374

187 crickets and 374 grasshoppers

Homework Solutions16) Let a = number of adult tickets

Let c = number of children’s tickets

a + c = 150 4.75a + 4.75c = 712.507.50a + 4.75c = 891.25 – 7.50a + 4.75c = 891.25

– 2.75a = – 178.75

a = 65 a + c = 150

(65) + c = 150 c = 85

65 adult and 85 children’s tickets were sold.

Homework Solutions17) Let b = number of balcony tickets sold

Let f = number of floor tickets sold

b = 100 + f4b + 12f = 3056

4(100 + f) + 12f = 3056400 + 4f + 12f = 3056400 + 16f = 305616f = 2656 f = 166

266 balcony tickets were sold.

b = 100 + fb = 100 + (166)b = 266

Vanessa has $9.75 in dimes and quarters. If she has 75 coins, how many of each type of coin does she have?

Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister. He used twice as many 32-cent stamps as 20-cent stamps. Determine how many of each type of stamp he used.

Ben had twice as many nickels as dimes. Altogether, Ben had $4.20. How many nickels and how many dimes did Ben have?