Math word problem

you work at a movie theater and keep track of ticket sales. on day 1 you sold 30 regular admission tickets and
20 senior citizen tickets for a total of $400. day two you sell 40 regular admission tickets and only 10 senior
citizen tickets for a total of $450. what is the cost of a regular admission ticket and a senior citizen ticket?

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5

Let "r" be the cost of one regular admission ticket

Let "s" be the cost of one senior citizen ticket

Given that,

On day 1 you sold 30 Regular Admission tickets and  20 Senior Citizen tickets for a total of $400

So we can frame a equation as:

30 Regular Admission tickets x cost of one regular admission ticket + 20 Senior Citizen tickets x cost of one senior citizen ticket = $ 400

30r + 20s = 400 ----- eqn 1

Day two you sell 40 Regular Admission tickets and only 10 Senior  Citizen tickets for a total of $450

So we can frame a equation as:

40 Regular Admission tickets x cost of one regular admission ticket + 10 Senior Citizen tickets x cost of one senior citizen ticket = $ 450

40r + 10s = 450 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "r" and "s"

Multiply eqn 2 by 2

80r + 20s = 900 --- eqn 3

Subtract eqn 1 from eqn 3

80r + 20s = 900

30r + 20s = 400

(-) ---------------------

50r = 500

Substitute r = 10 in eqn 1

30r + 20s = 400

30(10) + 20s = 400

300 + 20s = 400

20s = 100

Thus we have:

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.