Elizabeth and her sister earned money shoveling snow over winter break. altogether, they shoveled for a total of 30 hours. jenna charged her customers $12 per sidewalk, and her sister charged $11 per sidewalk. if they earned $347.50 total, how many hours did each girl spend shoveling?

Elizabeth spent 17.5 hours and her sister spent 12.5 hours.

Step-by-step explanation:

Let x be the number of hours that Elizabeth shoveled and y be the number of hours that her sister shoveled.

Number of hours they shoveled = 30

So, x + y = 30 or

y = 30 - x

Jenna charged $12 per sidewalk.

So, her total earnings = 12x

Her sister charged $11 per sidewalk.

So, her total earnings = 11y.

Their total income = $347.50.

So, 12x + 11y = 347.5

Substitute y = 30 - x,

12x + 11(30 - x) = 347.5

12x + 330 - 11x = 347.5

x + 330 = 347.5

x = 347.5 - 330

x = 17.5 and

y = 30 - x = 30 - 17.5 = 12.5.

Hence, Elizabeth spent 17.5 hours and her sister spent 12.5 hours.

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