Question

Hi I need help with 58 and 59. thank you in advance

22 58) The Blikony People have a monthly ritual of making payments to the King. The King sits atop his castle, where there are 20 steps, and then the 21" step gets you to the top where the King awaits. When a peasant makes their payment, they must leave 1 quarter on the first stair, 2 on the second, 3 on the third, and so on for the 20 steps. When they arrive to the King, they must give the King half of the money in their pocket. On the way down, the peasant is allowed to pick up any money on stairs that have whole-dollar amounts (i.e. $1, $2, etc.). When the peasant gets to the bottom, he now has $59 in his pocket. How much did he start with? 59) Jimbo has a lot of pets, including two dogs, Rocky and Toby. If you take the product of the number of fish, times the number of dogs, times the number of horses, times Jimbo's age (which is a higher number than the rest), the product is 1218. Knowing that he has more fish than horses, how many fish does he have? 2 DOGS 2

Answer 1

59)dogs=2

fish =f

horse=h

age of jimbo=j

f*2*h*j=1218

f*h*j=609

since 609 has prime factor 3*7*29

and j>f>h

so j=29

h=3 and number of fish=7

58)Let the money he starts with =x

there are 20 steps on which money has to left and then picked in return jouney

left money:

for the first step =x/4

remaining=x-x/4 = 3x/4

for second step = (1/2)(x)=3x/8

remaining= 3x/4-3x/8=3x/8

for third step=(3/4)(3x/8)=9x/32

remaining=(3x/8)-(9x/32)=3x/32

for 4th step=3x/32

remaining=6x/32 =3x/16

for 5th step=(5/4)(3x/16)=15x/64

remaining=-3x/64

since the money cannot be negative so he could not keep it on fourth step

so money left with him =3x/16

now he has to pay half of it to the king

so left money=3x/32

now he has to pick the whole amount of dollar

on 4th,3rd ,2nd and 1st step

59=3x/32 + whole dollar amount

x=(59-whole amount)32/3

Answer 2

Answer to #58 (Blikony)

Place a quarter on the first step, two quarters on the second step, and so forth. The dollar amounts on each step are as follows: .25, .50, .75, 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, 3.25, 3.50, 3.75, 4.00, 4.25, 4.50, 4.75 and on the 20th step there would be 5.00. That total is $52.50. 

On the way down, the peasant takes money from the steps with whole dollar amounts ($1, $2, $3, $4, and $5) which total up to be $15. 

We are told the peasant ends up with $59. So let's work backward. In the end, the peasant has $59. They earned $15 from the way down, so at one point the peasant had $44 at the top of the steps. The King also took half of his money at the top, so at one point the peasant had $88. Lastly, the peasant had to pay $52.50 to get to the top, so the peasant originally had $140.50.