MATH WORD PROBLEM
1 answer:
cost of one regular admission ticket = $ 10
cost of one senior citizen ticket = $ 5
<h3><u>Solution:</u></h3>Let "r" be the cost of one regular admission ticket
Let "s" be the cost of one senior citizen ticket
Given that,
<em><u>On day 1 you sold 30 Regular Admission tickets and 20 Senior Citizen tickets for a total of $400</u></em>
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
<em><u>Day two you sell 40 Regular Admission tickets and only 10 Senior Citizen tickets for a total of $450</u></em>
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
<em><u>Let us solve eqn 1 and eqn 2 to find values of "r" and "s"</u></em>
Multiply eqn 2 by 2
80r + 20s = 900 --- eqn 3
Subtract eqn 1 from eqn 3
80r + 20s = 900
30r + 20s = 400
(-) ---------------------
50r = 500
<h3>r = 10</h3>Substitute r = 10 in eqn 1
30r + 20s = 400
30(10) + 20s = 400
300 + 20s = 400
20s = 100
<h3>s = 5</h3><em><u>Thus we have:</u></em>
cost of one regular admission ticket = $ 10
cost of one senior citizen ticket = $ 5
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Answer:
There were 49 students in the class
Step-by-step explanation:
To solve this problem, we must build the Venn's Diagram of this set.
I am going to say that:
-The set A represents the students that watched TV on Monday
-The set B represents the student that watched TV on Tuesday.
-The set C represents the students that watched TV on Wednesday.
We have that:
In which a is the number of students that only watched TV on Monday, is the number of adults that watched TV both on Monday and Tuesday,
is the number of students that watched TV both on Monday and Wednesday, and
is the number of students that watched TV on every day.
By the same logic, we have:
This diagram has the following subsets:
The sums of all of this values is the number of student that were there in the class. This means that we want to find the value of T:
We start finding the values from the intersection of three sets.
Solution:
12 students watched TV on all three days:
14 students watched TV on both Monday and Tuesday
Of those who watched TV on only one of these days, 13 choose Monday, 9 chose Tuesday, and 10 chose Wednesday.
29 students watched television on Monday:
24 on Tuesday
Now we have every value needed to find T:
There were 49 students in the class