The time at which the cost for the services of the two companies would be in exactly 6 days. If we would compare the two charges, we would see that company A just charges 40 per day while B has a charge of 60, which is a standard fee, and a rate of 30 per day. So if we compute 40 x 6, we will have a total cost now of 240. If we compute 30 x 6, we will have a total cost now of 180 plus 60 which is the standard fee, and we will get 240. So in 6 days, the rates of the two companies would both accumulate to 240.
Answer:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Step-by-step explanation:
At first we translate mathematically each sentence:
(i) <em>Ali, Carrie and Bryan received a sum of money. </em>
- Ali's money.
- Bryan's money.
- Carrie's money.
(ii) <em>Bryan's money was </em>
<em> of Ali's money</em>.
(1)
(iii) <em>The ratio of Ali's money to Carrie's money was 4 : 1</em>.
(2)
(iv) <em>Ali had $ 160 more than Bryan</em>.
(3)
After some algebraic handling, we have the following system of linear equations:
(1b)
(2b)
(3b)
The solution of the system is:
,
, 
The sum of money is:


The sum of money received by Ali, Carrie and Bryan is $ 740.
The numerators = 3n ( where n = sequence number of the term
The denominators = n + 3
Answer is 3n / (n + 3)
Answer:
$13.50
Step-by-step explanation:
<u><em>2 bags of cat food = $4.50</em></u>
<u><em>1 bag of cat food = 2/4.50</em></u>
<u><em>= 2.25</em></u>
<u><em>6 bags of cat food = 2.25*6</em></u>
<u><em>=13.50</em></u>
Answer:
-0.9090... can be written as
.
Explanation:
Any <em>repeating </em>decimal can be written as a fraction by dividing the section of the pattern to be repeated <em>by </em>9's.
We can start by listing out
0.909090... = 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now. we let this series be equal to x, that is
= 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
Now, we'll multiply both sides by 100
.
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + ...
Then, subtract the 1st equation from the second like so:
= 90 + 0 + 9/10 + 0/100 + 9/1000 + 0/10000 + 9/100000 + 0/1000000 + ...
= - 9/10 - 0/100 - 9/1000 - 0/10000 - 9/100000 - 0/1000000 - ...
And we end up with this:

Finally, we divide both sides by 99 in order to isolate x and get the fraction we're looking for.

Which can be reduced and simplified to

Hope this helps!