Question

MATH WORD PROBLEM

Answer 1

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5

Solution:

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

$30 \times r + 20 \times s = 400$

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

$40 \times r + 10 \times s = 450$

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

r = 10

Substitute r = 10 in eqn 1

30r + 20s = 400

30(10) + 20s = 400

300 + 20s = 400

20s = 100

s = 5

Thus we have:

cost of one regular admission ticket = $ 10

cost of one senior citizen ticket = $ 5