Question

George's page contains twice as many type words as Bill's paid and Bill's page contains 50 fewer words and Charlie's page. If each person can type 60 words per minute,after one minute, the difference between twice the number of words on bills page and the number of words on Charlie's paid 210. How many words did bills page contain initially?

Answer 1

For this, we use simultaneous equations. Let George's page be g, Charlie's be c and Bill's page be b.

First, George's page contains twice as many type words as Bill's.

Thus, g = 2b.

Second, Bill's page contains 50 fewer words than Charlie's page.

Thus, b = c - 50.

If each person can type 60 words per minute, after one minute (i.e. when 60 more words have been typed) the difference between twice the number of words on bills page and the number of words on Charlie's page is 210.

We can express that as 2b - c = 210.

Now we need to find b, since it represents Bill's page.

We can substitute b for (c - 50) since b = c - 50, into the equation 2b - c = 210. This makes it 2(c - 50) - c = 210.

We can expand this to 2c - 100 - c = 210.

We can simplify this to c - 100 = 210.

Add 100 to both sides.

c - 100 + 100 = 210 + 100

Then simplify: c = 210 + 100 = 310.

Now that we know c, we can use the first equation to find b.

b = c - 50 = 310 - 50 = 260.

260 is your answer. I don't know where George comes into it. Maybe it's a red herring!

Answer 2

Answer:

320

Step-by-step explanation:

Let g be the number of words on George's page.  We know that George's page contains twice as many as Bill's; letting b represent Bill's page, this gives us

g = 2b

Bill's page contains 50 fewer words than Charlie's page; letting c represent Charlie's page, this gives us

b = c-50

Each person can type 60 words per minute.  After 1 minute, Bill's page would be represented by b-60 and Charlie's would be c-60.

The difference between twice the number of words on Bill's page, 2(b-60), and Charlie's page, c-60, is 210:

2(b-60)-(c-60) = 210

Substituting c-50 for b,

2((c-50)-60)-(c-60) = 210

2(c-50-60)-(c-60) = 210

2(c-110)-(c-60) = 210

2c-220-c--60 = 210

2c-220-c+60 = 210

Combining like terms,

c-160 = 210

Add 160 to each side,

c-160+160=210+160

c = 370

Charlie's page had 370 words on it; this means Bill's had 50 fewer, or 370-50 = 320.