One year ago liz was three times as old as her brother jack. in two years she'll be only twice as old as jack. how old are liz and jack now?

L = liz's age now

J = Jack's age now

L-1 and J-1 are their ages one year ago

L-1=3(J-1)

L-1=3J-3

L=3J-3+1

L=3J-2 (to be used later)

L+2 and J+2 are their ages in two years

L+2=2(J+2)

replace L by 3J-2

3J-2+2=2(J+2)

3J=2J+4

3J-2J=4

J=4 is Jack's age now

L-1=3(J-1)

L-1=3(4-1)

L-1=3*3

L-1=9

L=9+1

L=10 is Liz's age now

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages