Jessica has 4 times as many books as john and five times as many as karen. If Karen has more than 40 books what is the least number of books she can have?

Question

Jessica has 4 times as many books as John and five times as many as Karen. If Karen has more than 40 books what is the least number of books she can have?

Answer 1

Tom,

You're right: 220 books. Isn't 200 divisible by 4 and by 5? Why does it have to be 220? To answer my own question, It's not equal to 200 books but greater than 200. So 220 is the smallest number that can be divisible by 4 and 5 that is greater than 200.

Tom D

 

Answer 2

let x = number jessica has

 

x/5>40

 

x >200  but we need a value of x that is also divisible by 4 and 5

 

so

 

what is a number >200 that is also divisible by 4 and 5

 

that would be 220

 

so

 

Jessica has 220 books

 

John has 55 books

 

and Karen has 44 books

 

 

 

 

 

 

 

 

Answer 3

jessica = 4john

Jessica = 5karen

Karen > 40

let x = # of books for Jessica, y =John, z= karen's> 40

z =5x >= 40, x>=8

x=8, y= 32, z= 40

they're in a ratio of 1:4:5

x +4x +5x

with x= an integer

1, 4,5

2,8,10

3, 12,15

4, 16,20

5, 20,25

6, 24,30

7, 28, 35

8, 32, 40

9, 36, 45 = minimum for Karen

if Karen had 44, Jessica would have 44/5 =8.8 books and John gets 8.8(4) = 35.2 books

if fractional books were allowed 41 would also work, also 40+ epislon 40+ 1/infinity