DAY 386

When could these equations be true?

6 + 24 =1

5 + 5 = 2
23 + 60 =1
2 + 1 = 1
10 + 4 = 2

Answers:

6 days + 24 hours = 1 week

5 fingers/toes + 5 fingers/toes = 2 hands/feet
23 hours + 60 minutes = 1 day
2 dimes + 1 nickel = 1 quarter
10 o'clock + 4 hours  = 2 o'clock

DAY 385

Tom: Give me four and we'll each have the same.

Jane: Give me four and I'll have twice as many as you.

How many does each have?

Answer:

Tom has 20 and Jane has 28 ............ If gaining four will make Tom and Jane equal, Jane must have 8 more than Tom.

Let x = Tom

Let x + 8 = Jane

2(x-4) = x + 12

2x - 8 = x + 12

x = 20

x + 8 = 28

OR

Let x = Jane

Let x - 8 = Tom

2(x-12) = x + 4

2x - 24 = x + 4

x = 28

x - 8 = 20

DAY 384

When could these equations be true?

1 + 1 = 1

30 + 30 = 1

Answers:

1 foot + 1 foot + 1 foot = 1 yard

30 seconds + 30 seconds = 1 minute

or

30 minutes + 30 minutes = 1 hour

DAY 383

Three men eat three steaks in three days. How many steaks will six men eat in six days?

Answer:

12 ......... If three men can eat three steaks in three days, each man can eat one steak in three days .......... or two steaks in six days. Six men could eat six times that number of steaks in six days, or 12 steaks.

DAY 382

Consider the digits 1 - 9. They can be arranged in 9! ways. If you were to write down all of these possible arrangements on individual cards and then pick one, what is the possibility that the number you picked would be prime?

Answer:

Zero .......... In any nine-digit number using each of the digits once, the sum of the digits would be 45 (1+2+3+4+5+6+7+8+9 = 45). According to the rules of divisibility, any number in which the digits add up to a multiple of 9, is divisible by 9, and therefore not prime. Since 45 is a multiple of 9, the nine-digit number could not be prime.