Yesterday, two friends went into a bank to open savings accounts. allie started by putting $783 in her account, and she will deposit an additional $27 each week. nick made no initial deposit, but he will add $288 more each week. in a few weeks, the friends will have the same account balance. what is that account balance? how many weeks will that take?

Both accounts of Nick and Allie will have same amount of $864 in time period of 4 weeks.

Solution:

Given, Yesterday two friends went into a bank to open savings accounts.  

Allie started by putting $783 in her account, and she will deposit an additional $27 each week.  

Nick made no initial deposit, but he will add $288 more each week.  

In a few weeks, the friends will have the same account balance.  

Here, account balance of Allie for every week forms an A.P as

783, 810, 837, ……. With common difference 27

And, account balance of nick for every week will be  

0, 288, 576, …….. with common difference 288

Let, after n weeks the balance in both accounts be equal.

Then, nth term of both series will be equal, we know that, nth term tn of A.P is a + (n – 1)d  

Where, a is first term, d is common difference and n is number of terms.

Now, nth term of allie series = nth term of nick series.

783 + (n – 1) x 27 = 0 + (n – 1) x 288  

Here, we used same n for both sides because n represents number of weeks and it is common to both

783 + 27n – 27 = 288n – 288

756 + 288 = 288n – 27n

261n = 1044

n = 4.

So, it will take 4 weeks to have same balance and now, substitute n value in nth term of nick series.

Hence, both accounts will have same amount of $864 in time period of 4 weeks

answer is x<

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