these are some logic problems that i just cant figure out?

Question

a man went into a bank to cash a check. in handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. he pocketed the money without examining it and spent a nickel on his way home. he then found that he possessed exactly twice the amount of the check. he had no money in his pocket before going to the bank. what was the exact amount of the check?



"how old are you robinson?" asked colonel crackham one morning. "well, i forget exactly," was the reply; "but my brother is two years older than me; my sister is four years older than him;my mother was twenty when i was born; and i was told yesterday that the average age of the four of us is 39 years."
what was robinson's age?

but... he didnt spend 10 cents, he spent a nickel. nickel=5 cents

Answer 1

the second part,

Let robinson's age be x
brother's age = x+2
sister's age = x+6
mother's age = x+20

Average age is 39
Total age is 39*4=156

x + (x+2) + (x+6) + (x+20) = 156
4x + 28 = 156
4x = 128
x = 32

He is 32 years old

Answer 2

Age problem working on first one
R= Robinson B=Brother S=Sister M=Mother
R+B+S+M=39 x 4
B=R+2
S=R+6
M=R+20
R+(R+2)+(R+6)+(R+20)=156
4R+28=156
4R=128
R=32yrs

Answer 3

check was x dollars and y cents, guy got y dollars and x cents and spent 10 cents, so:

100y+x-10=2(100x+y), x and y integer and less than 100

199x-98y+10=0
y=(199x+10)/98

try plugging in iteger x's (or y's) to see if any of them results in an integer answer


(x + x+2 + x+4 + x+20)/4 = 39

x=(39*4-26)/4

Answer 4

brother=x+2
sister=(x+2)+4
mom=20 + (x+2)
39=(x+brother+sister+mom) / 4

Answer 5

@knight: No he spent a nickel, so that should be:

100y+x-5=2(100x+y)
100y+x-5=200x + 2y
98y-5=199x
y = (199x+5)/98