answer(non-routines problems)

ANSWERS:
1. Let x = the smaller number
y = the larger number
Equation:
Four times the smaller is five less than the larger
4x = 55 - x – 5
Solving:
4x = 55 - x - 5
4x + x = 55 - 5
5x = 50
x = 10 - the smaller number
55 - x = 45 - the larger number

2. Let u = units digit of original number
t = tens digit of original number
10t + u = original number
10u + t = new number
Equation:
(a) The sum o the digits is 10
t + u = 10
(b) The new number is less than the original number
10u + t = 10t + u - 18 or 9u - 9t = -18
Solving:
9u + 9t = 90 (multiply eq. 1 by 9)
9u - 9t = 18
18u = 72
u = 4
t + u = 10
t = 10 - 4
t = 6
Therefore, 10t + u = 10(6) + 4
= 60 + 4
= 64 -- original number

3. Let x = Gustav’s present age
y = Father’s present age

PRESENT PAST (A year ago)
GUSTAV x x - 1
FATHER y y - 1
Equations:
(a) Father is seven times as old as Gustav
y = 7x
(b) Father was nine times as old as Gustav
y - 1 = 9(x - 1) or y - 9x = -8

Solving:
Substitute 7x in place of y in eq. 2.
7x - 9x = -8
-2x = -8
x = 4
Therefore, Gustav’s present age is 4 years.

4. SECRET/NOTE:
Subtract 444 from the final answer, and then group the digits of the resulting number in pairs from right to left.

______ ______ ______ _______ __________
(month) (day) (year)
Suppose:
a. Multiply the number of the month of your birth by 100. (9 x 100 = 900)
b. To this product, add the day of the month of your birth. (900 + 24 = 924)
c. Multiply this sum by 2. (924 x 2 = 1,848)
d. Add 8 to this product. (1,848 + 8 = 1,856)
e. Multiply the sum by 5. (1,856 x 5 = 9,280)
f. Add 4 to the product. (9,280 + 4 = 9,284)
g. Multiply the sum by 10. (9,284 x 10 = 92,840)
h. Add 4 to this product. (92,840 + 4 = 92,844)
i. Add your age to this sum. (92,844 + 18 = 92,862)
j. Tell me your final answer. (92,862)
k. You are ____ years old and your birthday is on (month) and (year) (18, 09, 24)

Therefore, you are 18 years old and your birthday is on 09(month) and 24(day).

5. 19,419 – 13,882 = 5537
.’. Then, turn your calculator upside down, you will read there LESS

6. 2,101 x 18 = 37818
.’.Turn your calculator upside down, the word displayed is BIBLE

7. 256 x 209 = 53504
.’.Turn your calculator upside down, the word displayed is HOSES

8. The sum of the product is always
(B – 1) • 10,000 + A
that is, 1 less than the volunteer’s second number placed next to his or her first number.






Suppose:
If the volunteer chooses 4562 and 8234, the sum will be 82,334,562 since;
(B – 1) • 10,000 + A
= (8234 – 1) • 10,000 + 4562
= (8233) • 10,000 + 4562
= 82, 330, 000 + 4562
= 82, 334, 562

9. SECRET/NOTE:
Hint: Find the difference between the first and second values of the expression and the difference of the second and third values of the expression. Then find the difference of the 2 resulting number.

A = third difference/2
B = first difference – A
C= first value given by volunteer

10. Since 6 = VI and 11 = XI, therefore;
Show 6 and 6 make 11
VI and VI make XI
XI makes XI

11. We can analyze in this way. Two tiles are added to make each new figure – one tile to the top and another to the right side. To make the tenth figure, two tiles must be added six times to the seven tiles of the fourth figure. So there will be 7 + (2 x 6) = 7 + 12, or 19 tiles in the tenth figure.

9th figure…