Alice reads an equal number of pages of a storybook each day. After 8days, she has 5/6 of the storybook left to read. Another 4days, she has 180 pages left. How many pages are the in the storybook?
x = numbers of pages in the storybook
5 / 6 of the storybook left to read mean:
After 8 days, Alice read:
x - 5 x / 6 of the storybook
x - 5 x / 6 =
6 x / 6 - 5 x / 6 =
x / 6
After 8 days Alice read x / 6 of the storybook.
x / 6 per 8 days
( x / 6 ) / 8 =
x / 6 ∙ 8 =
x / 48 pages per day
She read:
x / 48 pages per day
For another 4 days she read:
4 ∙ x / 48 =
4 x / 4 ∙ 12 =
x / 12
of the storybook.
Totaly she read:
x / 6 + x / 12 =
2 x / 2 ∙ 6 + x / 12 =
2 x / 12 + x / 12 =
3 x / 12 =
3 x / 3 ∙ 4 =
x / 4
Totaly she read x / 4 of the storybook.
Pages left:
x - x / 4 =
4 x / 4 - x / 4 =
3 x / 4
( 3 / 4 ) x pages left
180 pages left mean :
3 x / 4 = 180
Multiply both sides by 4
3 x = 4 ∙ 180
3 x = 720
Divide both sides by 3
x = 720 / 3 = 240
240 pages
Proof:
She read:
x / 48 pages per day =
240 / 48 = 5 pages per day
After 8 days she read:
8 ∙ 5 = 40 pages
After next 4 days she reed:
4 ∙ 5 = 20 pages
Totaly she read:
40 + 20 = 60 pages
Pages left:
240 pages - 60 pages = 180 pages
A share of stock in a certain company is selling at Php . Find the cost of one share of stock rounded to the nearest hundredths.
Let's say Alice reads 'x' pages of the storybook each day.
After 8 days, she has 5/6 of the storybook left to read. This means she has only 1/6 of the storybook remaining to read, because 1 - 5/6 = 1/6.
So, after 8 days, she has read 8x pages, and this is equal to 1/6 of the total number of pages in the storybook.
Thus, we can write the equation: 8x = (1/6) * T, where T represents the total number of pages in the storybook.
Next, after another 4 days, she has 180 pages left to read. At this point, she has read a total of 12 days, or 12x pages.
Therefore, we can write another equation: 12x = T - 180.
Now, let's solve these two equations simultaneously to find the value of T, which represents the total number of pages in the storybook.
From the first equation, we can isolate T: T = 8x / (1/6) = 8x * 6 = 48x.
Substituting this into the second equation, we get: 12x = 48x - 180.
Simplifying, we have: 48x - 12x = 180, or 36x = 180.
Dividing both sides by 36, we find: x = 180 / 36 = 5.
Therefore, the number of pages in the storybook (T) is: T = 48x = 48 * 5 = 240.
So, there are 240 pages in the storybook.
To solve this problem, we'll set up a system of equations based on the information given.
Let's assume that the total number of pages in the storybook is "x". Since Alice reads an equal number of pages each day, we can represent the number of pages she reads each day as "y".
According to the problem, after 8 days, Alice has 5/6 of the storybook left to read. This means she has already read 1 - 5/6 = 1/6 of the storybook.
Since Alice reads an equal number of pages each day, in 8 days, she has read a total of 8y pages. Since this is 1/6 of the storybook, we can set up the equation:
8y = 1/6 * x
Similarly, after another 4 days, Alice has 180 pages left to read. In these 4 days, she reads a total of 4y pages. This means she has already read x - 180 pages.
So, we can set up the equation:
4y = x - 180
Now, we have a system of two equations:
Equation 1: 8y = (1/6) * x
Equation 2: 4y = x - 180
We can solve this system of equations to find the values of "x" and "y".
First, let's simplify Equation 1 by multiplying both sides by 6:
48y = x
Now, let's substitute this value of "x" into Equation 2:
4y = 48y - 180
Subtract 48y from both sides:
-44y = -180
Divide both sides by -44:
y = 4.09 (rounded to two decimal places)
Now that we have the value of "y", we can substitute it into either Equation 1 or Equation 2 to find "x". Let's use Equation 1:
48 * 4.09 = x
x = 196.92 (rounded to two decimal places)
Therefore, the total number of pages in the storybook is approximately 196.92.