2) Rick is planning the semi-annual golf tournament for the Wiley School of Busi

Question

2) Rick is planning the semi-annual golf tournament for the Wiley School of Business. The tradition is to have two different entry fees – a higher one for faculty ($35) and a lower one for staff and doctoral students ($25). The golf course charges $31 per entrant regardless of faculty and staff designation.

After all entries have been received, 7 full foursomes have entered (i.e., 28 golfers). After writing a check to the golf course to cover the golf fees, Rick has $12 left over in surplus funds to buy a few gag prizes. How many faculty and how many staff/doctoral students entered the golf tournament?

3) Your niece was born on the same day as you, just years apart. Six years ago, she was half you age. You are 25 years older than her. Determine the present age of both you and your niece. Show your work algebraically.

4) A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?

5) A friend brought small bags of cookies to sell at a fairly large Holiday Bowl Game Watch Party. Three kinds of cookies were sold: Stars (sold for $1 per bag), Circles (sold for $0.75 per bag) and Stars and Stripes (sold for $1.50 per bag).

He brought the cookies to the Watch Party in three large boxes that were totally filled to capacity. By volume, it is a known fact that each bag of Stars fills up 1% of a box (1/100th), each bag of Circles fills up 1/120th of a box while each bag of Stars and Stripes fills up 1.25% of a box (1/80th). HINT: Don’t concern yourself with what each box held; view this as an aggregate limit of numbers of cookies..

All cookies brought were sold, a total of 300 bags. The total amount of money raised was $312. All bags of cookies brought in the boxes were sold.

Can you determine how many of each of the three cookie types were brought/sold?

Explanation / Answer

Q2) Total money paid to the Golf course to cover the golf fees = 31*28 = $ 868

Total money earned = 868 + 12 = $ 880

Let Number of entreis received from Faculty and Staff & Doctoral students are F and S respectively

So, we have two linear equations,

35*F + 25*S = 880 ---- (1)

F + S = 28 ---- (2)

Solving the above two linear equations, apply operation (1) - 25*(2)

35F - 25F + 25S - 25S = 880 - 25*28

10F = 180

F = 18

S = 28-18 = 10

Number of Faculty = 18

Staff and doctoral students = 10

3) Let my present age = X

Niece's present age = X - 25

My age six years ago = X - 6

Niece's age six years ago = X - 25 - 6 = X - 31

X - 31 = (X - 6)/2

X - 31 = X/2 - 3

X/2 = 31 - 3

X = 56

Therefore, my present age = 56 years

Niece's present age = 56-25 = 31 years

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