Purchase Order Quantity
08/01/2001
by K.H. "Wicks" Wickremasinghe
JCN Company's beginning inventory was reduced by 10 percent and 3 units during the first week's sales. The second week's sales were 5 percent and 8 units of the inventory at the end of the first week. The third week's sales were 10 percent and 8 units of the inventory at the end of the second week. Having reached the purchase order quantity, they placed a purchase order for 40 percent and 4 units of the balance at the end of the third week. This brought the quantity in stock to the beginning inventory.
What is JCN's beginning inventory?
Grand Prize Winners
Congratulations to Brent Lybrand of Specialty Electronics (Landrum, S.C.) for solving "The New Neighbors," and to Dennis Tebaldi of BFGoodrich Aerospace (West Hartford, Conn.) for solving CrossNumber 63.
CrossNumber 65
Each clue, except 7 Down, is defined in terms of one or more of the four variables, W, X, Y and Z. Find the values of W, X, Y and Z. Also show the complete solution. No number is repeated.
Across
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1. X x Y
3. 2 x W
5. Z3
8. 10 x (W + X + Y + Z)
9. 5 x (Y + Z)
12. W x Y x Z
14. X3
15. 2 x Z
Down
1. X4
2. 4 x (W2) + 2 x (Z2) + X
4. Z2 - W2
6. X x Y2
7. A palindromic number
10. Y x (Z + 2 x X)
11. Z
13. 7 x Z
Contest Rules: All entries must be received by August 27, 2001. The winners of the word puzzle and CrossNumber (can be the same person) will be drawn from all correct entries. Fax all entries to 847-634-4240. All entries must include name, complete address, company affiliation and daytime phone number to be considered.
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Solutions to June's Puzzles
CrossNumber 63
The New Neighbors
Answer: Father 40, Mother 42, Jack and Jill 12, David 13 and Susan 5
Solution: Let ages of Father, Jack and David be denoted by b, c, d and Mother, Jill and Susan be denoted by a, c, e.
From the given clues,
b + c + d = 65 Equation (1)
a + c + e = 59 Equation (2)
In two years time:
b + 2 = 6(e + 2)
b - 6e = 10 Equation (3)
Two years ago:
a - 2 = 4(c - 2)
a - 4c = -6 Equation (4)
c years later:
d + c = e + c + 8
d - e = 8 Equation (5)
5 x Eq (1) + -1 x Eq (2) + -5 x Eq (3) + Eq (4) + -5 x Eq (5)
34e = 170; e = 5. Substituting for e in Eq (3), b = 40. Similar substitutions give a = 42, b = 40, c = 12, d = 13 and e = 5.