Hudson read 2 5 of a novel in the morning after reading 1 6 of the remainder in the afternoon he still had 170 more pages to read find the total number of pages in the novel.
Let's represent the total number of pages in the novel as x.
In the morning, Hudson read 2/5 of x, which is (2/5)*x.
The remainder of the novel is (1-2/5)*x = (3/5)*x.
In the afternoon, he read 1/6 of the remainder, which is (1/6)*(3/5)*x = (1/10)*x.
After reading in the afternoon, he still had 170 more pages to read, so:
(3/5)*x - (1/10)*x = 170
Multiplying through the equation by 10 to eliminate the fractions gives:
6x - x = 1700
Simplifying the equation gives:
5x = 1700
Dividing both sides of the equation by 5 gives:
x = 340
Therefore, the total number of pages in the novel is 340 pages.
To solve this problem, let's break it down step by step:
1. Let's assume the total number of pages in the novel is x.
2. The amount of pages Hudson read in the morning is 2/5 of x.
3. After reading 2/5 of the novel, Hudson still has 3/5 of the novel left to read.
4. The amount of pages he read in the afternoon is 1/6 of the remaining 3/5 of the novel, which is (1/6) * (3/5) * x.
5. After reading both in the morning and afternoon, Hudson still had 170 more pages to read. So, we can set up the equation:
(3/5)x - (1/6) * (3/5) * x = 170
6. To solve this equation, we'll multiply the denominators to eliminate fractions:
6*(3/5)x - 6*(1/6)*(3/5)x = 6 * 170
18/5 (or 3.6)x - 1/5 (or 0.2)x = 1020
7. Combining like terms, we have:
(18/5 - 1/5)x = 1020
(17/5)x = 1020
8. To isolate x, we'll multiply both sides by the reciprocal of (17/5), which is 5/17.
x = (1020)*(5/17)
x = 300
Therefore, the total number of pages in the novel is 300.
Let's break down the problem step by step:
Step 1: Hudson read 2/5 of the novel in the morning.
Let's say the total number of pages in the novel is "x".
In the morning, Hudson read (2/5)*x pages.
Step 2: Hudson read 1/6 of the remainder in the afternoon.
After reading 2/5 of the novel in the morning, the remaining pages are (3/5)*x.
In the afternoon, Hudson read (1/6) * (3/5)*x pages.
Step 3: Hudson still had 170 more pages to read.
After reading in the morning and afternoon, Hudson had (3/5)*x - (1/6) * (3/5)*x = (5/6)*(3/5)*x pages left to read.
According to the problem, this amount is equal to 170.
Step 4: Set up and solve the equation.
(5/6)*(3/5)*x = 170
First, simplify the left side of the equation:
(5/6)*(3/5) = 3/6 = 1/2
Now we have:
(1/2)*x = 170
To solve for x, we divide both sides of the equation by (1/2):
x = 170 / (1/2)
x = 170 * 2
x = 340
Therefore, the total number of pages in the novel is 340.