Saving Paradox

Algebra Level 1

Every month, Ivan spent $300 of this salary. He saves the remainder, which is 3 5 \frac{3}{5} th of his salary. What is his monthly salary?

[The options are in $. Sorry that he makes so little money, the answers must be from 0 to 999.]

180 120 500 750

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18 solutions

He saves the remainder, which is 3/5th of his salary. So which means he spent 2/5th of his salary.

2/5 of the total salary is $300

okay we used "a" as the total salary 2/5 x a = $300

eliminate the 2/5 by divide it

(2/5)/(2/5) x a = $300/(2/5)

a = $300 x 5/2 a = $750

Easy

Prayogi Aja - 7 years, 4 months ago

oh,,good solution...

THEJAS D - 7 years, 5 months ago

ohh ... gud one!!!!

Vivek RS - 7 years, 5 months ago
Daniel Chiu
Dec 14, 2013

The answer is his salary, which is also 300 plus 3 5 \dfrac{3}{5} of his salary. If x x is his salary, 300 + 3 5 x = x x = 750 300+\dfrac{3}{5}x=x\implies x=\boxed{750}

oh ! nice solution !!

Devesh Rai - 7 years, 5 months ago
Joseph Francisco
Dec 17, 2013

I made the fractions percentages to easily make use of the law of proportionality.

We know that 2/5 or 40% of his salary is 300.

40 : 300

but 3/5 or 60% of his salary is unknown and thereby I name it "S".

60 : S

Finding S,

40 : 300 = 60 : S

40S = 18000

S = 450

Obviously, adding the 2/5 of his salary with the 3/5 of it makes the whole of it.

2/5 is 450 and 3/5 is 300

450 + 300 = 750

Vivek Maurya
Dec 15, 2013

Let's take his salary to be, x then-- he spends $300 and saves, $(x-300), so, 2x/5=x-300 solving x=750

300/2=150= 1/5 of salary multiply by 5 to get the whole salary 750

Nick Nicolas
Apr 28, 2014

3/5 is equivalent to 60% and 2/5 is equivalent of course to 40%. By dividing $300 to .40 we get the total salary of $750.

Katrina Mayuga
Apr 6, 2014

300 is 2/5 of his salary -> from 5/5 (his salary) - 3/5 (savings) 300/2 = 150 150 x 5 = 750

Syed Ahsanuddin
Mar 28, 2014

3/5*x=x-300

x=750

very easy

2/5 from the salary are 300. so, the salary of him are 750

Raj Kumar
Jan 8, 2014

2x/5 = 300 so, x=750

Prasun Biswas
Dec 21, 2013

Since what he saves is 3 5 \frac{3}{5} th of his salary, so the money spent is ( 1 3 5 ) = 2 5 (1-\frac{3}{5}) = \frac{2}{5} th of his salary.

Let the salary be $x.

Now, 2 5 x = 300 x = 300 × 5 2 x = 150 × 5 x = 750 \frac{2}{5}x=300 \implies x=300\times \frac{5}{2} \implies x=150\times 5 \implies x=\boxed{750}

Raymond Julianto
Dec 18, 2013

He spent $300 He saves the rest(x),x=3/5 of his salary He spent=5/5- 3/5=2/5 of his salary 5/2*300=$750

Matheus Jun Ota
Dec 16, 2013

Let $x$ be Ivan monthly salary: $$x \frac{2}{5} = 300 $$ $$x = 300 \frac{5}{2} = 750 $$

Ritesh Surve
Dec 16, 2013

Saved money is 3/5th of salary
Thus,2/5th salary=money spent! If x is salary,then (2/5)x=300 x=(5/2)300=2.5*300=750

Walidur Mridul
Dec 16, 2013

suppose his salary is 'X' so according to the statement- X - 3X/5 = 300 then, X=750

Marcus Vinicius
Dec 16, 2013

If the amount of $300 is equal to 2/5 of his salary, then we only must write a simple equality to reach the result: (2/5)X = 300, then x= 750 How did i know that 300 is equal to 2/5 of the salary? Well, the introduction said that he only spends 300,00 of his salary, and all the rest is saved, which is equal to 3/5. If we think about the fraction theory just for a couple of seconds, we can realise that what is gone is equal to 1- (2/5) = 3/5.

3x/5=300 then x=750

Mansi Shrivastava
Dec 15, 2013

Let the salary be x , according to condition , total salary- expenditure= 3/5 of his salary i.e x-300=3/5x = 750

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