A 6000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $174,000?

Step-by-step explanation:

Let x be the amount of tickets sold for $25 and y be the amount of tickets sold for $40, since there are 6000 seats theatre then;

x+y = 6000 1

If x tickets cost $25 and y tickets are sold for $40 with total revenue of $174,000, then;

25x + 40y = 174,000 2

From 1, x = 6000-y 3

Substitute equation 3 into 2:

25x + 40y = 174,000.

25(6000-y) + 40y = 174,000

150,000-25y + 40y = 174,000

150,000+15y = 174,000

15y = 174,000-150,000

15y = 24,000

y = 24,000/15

y = 1600

Substitute y = 1600 into equation 3:

x = 6000-y

x = 6000-1600

x = 4400

Hence 4400 $25 tickets and 1600 $40 tickets must be sold to generate a revenue of $174,000

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.