# Where am I wrong in this algebraic equation?

The question is:

Some sweets were to be distributed equally among 175 people. When 35 people were not present, everyone got an extra sweet. How many sweet were available for distribution?

My solution is:

Let $x$ = number of sweets each one gets. Then, $175x = 140 (x+1)$. Solving we get $x = 4$. So the total number of sweets available is $175 \times 4= 700$.

The answer in my book is given as $2800$. Where am I wrong? Or am I right? Thank you. Update:- This is the solution given in my book:-( 7th) Where is the book's solution wrong?

• Next time, please use MathJax for users to understand the question more clearly. – Landuros Nov 4 '17 at 8:38
• You are right . – Rohan Nov 4 '17 at 8:42
• @GuyFsone sir i think you mean were. but the question says 175, how can the people be 70? – Ram Keswani Nov 4 '17 at 8:58
• because of the 35 remaining sweetes that rose the number of each people present to one. – Guy Fsone Nov 4 '17 at 9:01
• The book's answer is not only wrong, it promotes sloppy and dangerous writing. Obviously $x/140 - x/175$ is not equal to $5x-4x$. – aschepler Nov 4 '17 at 14:53

## 1 Answer

Are you sure that the answer in your book is correct? Just think about it. $2800\div175=16$. So, each person gets 16 sweets. Then, $2800\div(175-35)=20$. This, on the other hand, says that each person will get $4$ extra sweets if we subtract 35 people from the original number of people that were present. In your problem, however, it is stated that each person in that case should receive only one extra sweet. Do you see the problem? The answer in your book just can't be the solution to the original question. But actually your solution, $700$ sweets, is the correct one. I get the same answer.

Here's my solution:

Let $x$ be the total number of sweets. Then, $\frac{x}{175}$ is the number of sweets each person gets when there are 175 people. Likewise, $\frac{x}{140}$ is the number of sweets each person gets when there are only $175-35=140$ people. From what it says in the problem, we know that $\frac{x}{140}$ should be equal to $\frac{x}{175} + 1$ because when there were only $140$ people, everybody got one more sweet than when there were $175$ people. In other words, the number represented by $\frac{x}{140}$ is bigger than the number represented by $\frac{x}{175}$ by exactly one. Thus, we arrive at the equation $\frac{x}{140}=\frac{x}{175} + 1$ which we need to solve for $x$ whose value is going to be our total number of sweets that were available for distribution:

$$\frac{x}{140}=\frac{x}{175} + 1\implies\\ \frac{x}{140}-\frac{x}{175}=1\implies\\ 175x-140x=140\cdot 175\implies\\ 35x=24,500\implies\\ x=\frac{24,500}{35}\implies\\ x=700$$

Answer: $700$ sweets were available for distribution.

• thank you sir. The book must be wrong, there are plenty of wrong solutions in my book. – Ram Keswani Nov 4 '17 at 12:14
• sir can you see and tell where the book's solution is wrong. I updated the question. – Ram Keswani Nov 4 '17 at 12:20
• Personally, the solution in your book does not make a whole lot sense to me. – Michael Rybkin Nov 4 '17 at 12:52