# Linear equations algebra based problem

• zak100
In summary, the conversation revolves around a mathematical problem involving the number of English and French books read by Diana in 1999 and 2000. Various methods of solving the problem and finding the total number of books read are discussed, with a focus on correctly representing and solving for 60% of the total number of books read, which is assumed to be French. The correct solution involves using exact fractions rather than decimals.
zak100

## Homework Statement

I got following Question from a book:

I am doing it using a different method but my answer is wrong. Can somebody please guide me, what is the problem with it??
The question is:In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books that she read during the two years were French, how many books did she read in 2000?

## Homework Equations

Linear equation in single variable based problem

## The Attempt at a Solution

1999: E(10), F(7) = 17

2000: E(x), F(2x)

Two years total books = 10 + 7 + x + 2x

1.666x /*60 % */ + 2.5x /* 40 */ = 17 + 3x

4.166 - 3x = 17

X = 14.579

2x = 29

Total = 15 + 29 = 44 (wrong answer)

Some body please guide me.

Zulfi.

zak100 said:
If 60% of the books that she read during the two years were French, how many books did she read in 2000?

are you applying this condition correctly?
as the snag must lie here.

zak100 said:

## Homework Statement

I got following Question from a book:

I am doing it using a different method but my answer is wrong. Can somebody please guide me, what is the problem with it??
The question is:In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books that she read during the two years were French, how many books did she read in 2000?

## Homework Equations

Linear equation in single variable based problem

## The Attempt at a Solution

1999: E(10), F(7) = 17

2000: E(x), F(2x)

Two years total books = 10 + 7 + x + 2x

So far, so good.

1.666x /*60 % */ + 2.5x /* 40 */ = 17 + 3x
3x is the total number of books read in 2000 (3x = 2x [French] + x [English])

17 + 3x = total number of books read in 1999 and 2000.

How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?

Hi,
<How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>

I am trying to work in a different way:

According to the question, it says:
<If 60% of the books that she read during the two years were French>
60% is French so 40% should be english.
60% = 1.666
& 40% = 2.5
So 1.666x + 2.5x = 17 + 3x
I want to do it in this way. Please tell me what's wrong with it?

Zulfi.

zak100 said:
60% = 1.666
?? what does the above statement means?

zak100 said:
Hi,
<How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>

I am trying to work in a different way:

According to the question, it says:
<If 60% of the books that she read during the two years were French>
60% is French so 40% should be english.
60% = 1.666
& 40% = 2.5
So 1.666x + 2.5x = 17 + 3x
I want to do it in this way. Please tell me what's wrong with it?

Zulfi.

60% = 60/100, but you wrote 1.666 = 166.6/100!

If E = number of English books read in year 2000, then the total number of English books read in the two years is N_Eng = 10+E and the total number of French books read in the two years is N_Fr = 7+2E. Now 60% of the total is (6/10)(17 + 3E), and this is supposed to equal the number of French books read. Avoid decimals as long as possible; just work with exact fractions, except maybe at the last minute.

zak100 said:
Hi,
<How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>

I am trying to work in a different way:

According to the question, it says:
<If 60% of the books that she read during the two years were French>
60% is French so 40% should be english.
60% = 1.666
& 40% = 2.5
So 1.666x + 2.5x = 17 + 3x
I want to do it in this way. Please tell me what's wrong with it?

Zulfi.
You can do it your way or you can do it the right way -- yer cherce.

Don't expect your way to get you the correct answer, however.

Hi,
<60% = 1.666>
if you divide any number by 1,666 you would get 60% of that value. For instance if you divide like 200/1.66 you would get 120.48 which is approximately 60% of 200, & you can also write it:
120/200 * 100 ,
Similarly if you divide any number by 2.5 you would get 40% of that value.

If you want me to avoid decimal, i can write it:
60/100 x + 40/100 x = 17 + 3x
but x = 27
& 2x = 54
so total = 81 (not correct)
please tell me what's wrong with my solution.

<How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>
Instead of 60% i am considering 100% (i.e 60% French & 40% english) & making it equal to the total books read in 2 years. Why is this approach not possible?

Zulfi.

Last edited:
zak100 said:
Hi,
<60% = 1.666>
if you divide any number by 1,666 you would get 60% of that value. For instance if you divide like 200/1.66 you would get 120.48 which is approximately 60% of 200, & you can also write it:
120/200 * 100 ,
Similarly if you divide any number by 2.5 you would get 40% of that value.

If you want me to avoid decimal, i can write it:
60/100 x + 40/100 x = 17 + 3x
but x = 27
& 2x = 54
so total = 81 (not correct)
please tell me what's wrong with my solution.

<How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>
Instead of 60% i am considering 100% (i.e 60% French & 40% english) & making it equal to the total books read in 2 years. Why is this approach not possible?

Zulfi.

Your statement "if you divide any number by 1,666 you would get 60% of that value." is not true; but it is approximately true. Dividing by 1.6666666666666666666666666 would get you closer to a true statement, but no finite number of decimal places will give you an exact statement like the one you want. Of course, I know perfectly well that using 3 or 4 decimal places is often good enough in practice, but the point I am making is that you said something that is only approximately true, and I am not sure you actually realize that.

Ray Vickson said:
Your statement "if you divide any number by 1,666 you would get 60% of that value." is not true; but it is approximately true. Dividing by 1.6666666666666666666666666 would get you closer to a true statement, but no finite number of decimal places will give you an exact statement like the one you want. Of course, I know perfectly well that using 3 or 4 decimal places is often good enough in practice, but the point I am making is that you said something that is only approximately true, and I am not sure you actually realize that.
I'm frankly puzzled why anyone would want to divide to find 60% of something when this proportion can be as easily determined by multiplying the whole by 0.6.

zak100 said:
60% = 1.666
& 40% = 2.5
Don't write stuff like this -- neither one makes any sense.
60% of what equals 5/3?
40% of what equals 5/2?
There needs to be a variable in place of each what.

Hi,
Okay, 0.6 is also logical, so for question in this thread I have for the combine 2 years books read by her are:
0.6 + 0.4 = 17 + 3x but now i am getting the answer in minus.
Whats getting wrong when i am considering the whole 100%. There are only two books, if composition of french is 60% then composition of English should be 40% but why its not working.
Some body please tell me my mistake.
Zulfi.

zak100 said:
Hi,
Okay, 0.6 is also logical, so for question in this thread I have for the combine 2 years books read by her are:
0.6 + 0.4 = 17 + 3x but now i am getting the answer in minus.
Whats getting wrong when i am considering the whole 100%. There are only two books, if composition of french is 60% then composition of English should be 40% but why its not working.
Some body please tell me my mistake.
Zulfi.
Your mistake is that 0.6 + 0.4 = 17 + 3x is not the correct equation to use here.

To recapitulate the problem statement:
zak100 said:

## Homework Statement

In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books that she read during the two years were French, how many books did she read in 2000?
First of all, forget the 0.40. That doesn't come into consideration at all.

Figure out how many French books Diana read in 1999 and 2000, using what information is given in the statement above.

You are told she read 7 French books in 1999, and 10 English books. How many books did Diana read in 1999?

In 2000, Diana read twice as many French books as English books. Since the number of English books or French books read is unknown, you would pick one kind of book and say that Diana read x of them in 2000.

So, the next step here is to express the number of books which Diana read in 2000.

Write an expression for the total number of books Diana read in 1999 and 2000.

60% of this total number of books read is equal to the number of French books Diana read in 1999 and 2000. How would you express this?

Solve this last expression for x, and then calculate the number of books Diana read in 2000.

Hi,
Thanks for your reply & i appreciate all of you for helping me. Its a great forum & i am getting help immediately.
However if you are saying this:
<First of all, forget the 0.40. That doesn't come into consideration at all.>
Then it means the end of this thread. Because my interest in this question was particularly due to 40%. Otherwise the solution is mentioned in the book.
Any how I tried different options & it turns out that you people are right.

Zulfi.

## 1. What is a linear equation?

A linear equation is an algebraic expression that can be written in the form of y = mx + b, where m represents the slope and b represents the y-intercept. It is a straight line on a graph and is used to represent a relationship between two variables.

## 2. How do you solve a linear equation?

To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by using inverse operations, such as adding, subtracting, multiplying, and dividing. Once the variable is isolated, you can solve for its value by substituting it back into the equation.

## 3. What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to graph a linear equation and determine its slope and y-intercept.

## 4. What is the point-slope form of a linear equation?

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. This form is useful for finding the equation of a line when given a point and the slope.

## 5. What are some real-life applications of linear equations?

Linear equations are used in many real-life situations, such as calculating the cost of a cell phone plan based on the number of minutes used, determining the speed of a car over time, or predicting the growth of a population. They are also used in fields like economics, physics, and engineering to model and solve various problems.

• Precalculus Mathematics Homework Help
Replies
8
Views
913
• Precalculus Mathematics Homework Help
Replies
2
Views
995
• Precalculus Mathematics Homework Help
Replies
3
Views
2K
• Linear and Abstract Algebra
Replies
1
Views
113
• Precalculus Mathematics Homework Help
Replies
4
Views
1K
Replies
9
Views
2K
• Science and Math Textbooks
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
840
• Calculus and Beyond Homework Help
Replies
7
Views
1K
• Precalculus Mathematics Homework Help
Replies
9
Views
2K