Vincen wrote:Mr. and Mrs. Walters invited 90 people to their wedding. One-tenth of the attendees brought appliances as gifts, twenty percent of the attendees gave gift certificates as gifts, and the rest of the attendees gave cash. If only two-thirds of the invited guests attended, there were no uninvited guest and the average (arithmetic mean) cash gift was 175 dollars, how much cash did Mr. & Mrs. Walters receive?
A. $3,150
B. $7,350
C. $8,400
D. $9,450
E. $11,025
The OA is B.
What are all the calculation behind this PS question? I think there are too much percentages. Experts, help me please.
Hi Vicen,
Let's take a look at your question.
In the very first step let's review some important facts described in the question statement.
First Step:
Mr. and Mrs. Walters invited 90 people to their wedding.
Further, in the statement, it is told that "Only two-thirds of the invited guests attended and there were no uninvited guest"
Therefore, in the first step, we will calculate the number of guests who attended their wedding.
90×2/3
=30×2
=60
It means 60 guests attended their wedding.
Second Step:
The question states, "One-tenth of the attendees brought appliances as gifts".
Now, we will find the number of attendees who brought appliances as gift i.e one-tenth of the attendees.
60×1/10
=6×1
=6
6 guests brought appliances as gifts.
Third Step:
The question states, "twenty percent of the attendees gave gift certificates as gifts".
Now, we will find the number of attendees who gave gift certificates as gifts i.e twenty percent of the attendees.
60×20/100
=6×2
=12
12 gave gift certificates as gifts.
Fourth Step:
The question states, "the rest of the attendees gave cash".
Now, we will find the number of attendees who gave cash i.e the rest of the attendees.
Total Attendees - number of attendees who brought appliances as gift - number of attendees who gave gift certificates as gifts
= 60 - 6 - 12
= 42
Therefore, 42 attendees gave cash.
Fifth Step:
The question states, "the average (arithmetic mean) cash gift was 175 dollars, how much cash did Mr. & Mrs. Walters receive?".
We know that,
Average = (Sum of the quantities)/(Number of quantities)
Let's rewrite this formula according to our question statement,
Average cash gift = (Total Cash)/(Number of attendees who gave cash) ----- (i)
We will use this average formula to find out the total sum of cash Mr. & Mrs. Walters receive.
Average = 175 dollars
Number of attendees who gave cash = 42
Plugin the values in (i)
175 = (Total Cash) / 42
Total Cash = 175 x 42
Total Cash = 7, 350 dollars
Therefore, OPTION B is correct.
I am available if you'd like any followup.
