# help on this problem

#### noname

##### New member
Hello,

i found this question over the internet from an aptitude practice exam.
cant solve this problem..

below are the Question and Answer.

Q > if 2/5 of 3x=120, what is 1/5 of x?
A > First we find what 2/5 of 1x is by dividing 120 by 3=40.
if 2/5 of x=40, then 1/5 of x must be 40/2=20.

may i know what topic should i study so i can understand this problem?

Thanks

#### tkhunny

##### Moderator
Staff member
Basic Properties
----- Associative Property of Multiplication
----- Reciprocals, Multiplication
----- Commutative Property of Multiplication

(2/5)*3x = 120
2*(1/5)*3*x = 120
2*3*(1/5)*x = 120
(1/2)*2*3*(1/5)*x = (1/2)*120
1*3*(1/5)*x = 60
3*(1/5)*x = 60
(1/3)*3*(1/5)*x = (1/3)*60
1*(1/5)*x = 20
(1/5)*x = 20

Funny thing is, there is no need to "solve for x". One can answer the question directly.

#### Jomo

##### Elite Member
Hello,

i found this question over the internet from an aptitude practice exam.
cant solve this problem..

below are the Question and Answer.

Q > if 2/5 of 3x=120, what is 1/5 of x?
A > First we find what 2/5 of 1x is by dividing 120 by 3=40.
if 2/5 of x=40, then 1/5 of x must be 40/2=20.

may i know what topic should i study so i can understand this problem?

Thanks
3x=120, is the same as x = 40

Now that you know x, they are saying that 2/5 of x = 40

Now 1/5 is half of 2/5.

So to find 1/5 of x, 1/5 of 40 just compute half of 40 = 20.

Which step in any solution you viewed do you not understand?

#### JeffM

##### Elite Member
Hello,

i found this question over the internet from an aptitude practice exam.
cant solve this problem..

below are the Question and Answer.

Q > if 2/5 of 3x=120, what is 1/5 of x?
A > First we find what 2/5 of 1x is by dividing 120 by 3=40.
if 2/5 of x=40, then 1/5 of x must be 40/2=20.

may i know what topic should i study so i can understand this problem?

Thanks
As tkhunny and jomo indicated, this can be solved in a logical-arithmetical way. But most people with some mathematical training would solve it by algebra. The reason is that algebra removes a lot of complicated thought in solving problems that can be solved through a combination of logic and arithmetic.

A large part of the utility of algebra involves finding a number or numbers that satisfy certain quantitative constraints.

So we say that y = the number we want to know. What do we know about y? We are told (given) that

$$\displaystyle y = \dfrac{1}{5} * x.$$

OK, but what does x equal? Well, we are told that

$$\displaystyle \dfrac{2}{5} * 3x = 120 \implies \dfrac{1}{5} * (2 * 3x) = 120 \implies 2 * 3x = 5 * 120 = 600.$$

We used an algebraic technique called clearing fractions. In English, two fifths of something is the same as one fifth of that something doubled, and if one fifth of anything equals some number, then that anything must equal 5 times the number. It is just common sense in symbols reduced to simple rules.

$$\displaystyle 2 * 3x = 600 \implies 6x = 600 \implies x = 100 \implies 5y = 100 \implies y = 20.$$

Isn't that simple to follow? And that is why algebra is important to know.

#### math master

##### New member
3x=120, is the same as x = 40

Now that you know x, they are saying that 2/5 of x = 40

Now 1/5 is half of 2/5.

So to find 1/5 of x, 1/5 of 40 just compute half of 40 = 20.

Which step in any solution you viewed do you not understand?
that makes sense