Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Mr. and Mrs. Ahuja weigh $x$ kg and $y$ kg respectively. They both take a dieting course at the end of which Mr. Ahuja loses $5$ kg and weighs as much as the wife weighed before the course. Mrs. Ahuja loses $4$ kg and weighs $7$/$8$th of what her husband weighed before the course. From two equations in $x$ and $y$ and hence find their present weights.

I tried the following,

Mr. Ahuja's weight before the course$=$$x$ kg

Mrs. Ahuja's weight before the course$=$$y$ kg

                              After dieting course

Mr. Ahuja's weight: $E_1 =>x-5=y$

Mrs. Ahuja's weight: $E_2 =>y-4=\frac78 x$

Solving for $x$, I am getting $-27$ which is not possible.

Where did I go wrong? Please help.

share|cite|improve this question
Hmm, I get sensible answers. Giving you a first step, did you get $x = \frac{7}{8}x + 9$? – Jason Knapp Jul 29 '14 at 19:24

2 Answers 2

up vote 4 down vote accepted

$$y = x-5 \;\text{and}\; y - 4 = \frac 78 x \implies y - 4 = \underbrace{(x-5)}_{\large y} - 4 = \frac 78 x$$

Multiplying both sides of the equation by $8$ gives us $$\begin{align} 8(x-5) - 8\cdot 4 = 7x & \iff 8x - 72 -7x = 0 \\ &\iff x = 72\text{ kg}.\end{align}$$

Now solve for $y = x - 5 = 72-5 = 67\;\text{ kg}$.

Recall that $x, y$ give the weights prior to losing weight. So we need to find current weights: Mr: $x- 5 = 72 - 5 = 67$, Mrs: $67 - 4 = 63$.

share|cite|improve this answer
Perhaps I am wrong, but plugging $x=44$ back into the original equations doesn't work out. – Vincent Jul 29 '14 at 19:30
But the value of x in the back of the book is 67 kg. – Abhishekstudent Jul 29 '14 at 19:31
But the question was to find their present weights, which are $x-5$ and $y-4$. – Per Manne Jul 29 '14 at 19:59
Indeed, @PerManne! – amWhy Jul 29 '14 at 20:03
@Abhishekstudent Just to clarify. You (we) set up the problem using $x, y$ to represent Mr and Mrs's weights, respectively, prior to losing weight. We are given that Mr. lost 5 kg, and Mrs lost 4 kg. Thus, since we are asked to find their present weights, Mr's present weight is $72 - 5 = 67$ kg. Mrs's present weight is $67 - 4 = 63$ kg. That should explain the discrepancy. – amWhy Jul 30 '14 at 12:14



$y=\frac78 x +4$

Set them equal to each other, solve for $x$. Then substitute $x$ into one of the original equations to find $y$.

Should find that $x=72$ kg and $y=67$ kg.

share|cite|improve this answer
Yes! That's exactly what I am getting. But the answer is not matching the answer at the back of the book. The answer according to the book should be 67 and 63. – Abhishekstudent Jul 29 '14 at 19:34
You can see that $67$ and $63$ obviously do not work out. Plug them into the first equation and you can see that $67-5=62$, not $63$. – Vincent Jul 29 '14 at 19:35
@Abhishekstudent Read the question more carefully. $67$ and $63$ kg are the present weights of mr. and mrs Ahuja, i.e., after the dieting course. – Per Manne Jul 29 '14 at 19:56

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.