Import machine tools problem

In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

Total sales of imported tools form Japan = x
Total sales of all tools in US = y
so 45% of 25% of y = x
Read it as 25 of tools sold are imported of these 45% are of Japanese origin
so 25% of y , of these i.e (25/100)y, 45% or 45/100 are Japanese
so 25/100 x 45/100 y = x
Solve for y
IMO C

For easy calculation, let's take total sale T = 400%
imported = 100%.
Japnese = 45%

So, 45% of T = x
1% of T = x/45
400% of T = x/45 * 400
= 80x/9

IMO, E

this_time_i_will wrote:For easy calculation, let's take total sale T = 400%
imported = 100%.
Japnese = 45%

So, 45% of T = x
1% of T = x/45
400% of T = x/45 * 400
= 80x/9

IMO, E

Much simpler way:
Japanses Import sales X= 0.45 * 0.25 * Y

Total sales = Y
Express Y in terms of X
Y =(X/(.45 *.25)
=80X/9

IMO E

Sampits wrote:Hi experts,

I need your help... I have been dealing with this one for a while... I would appreciate some help on it:

In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

(A) 9x/80

(B) 13x/20

(C) 80/9x

(D) 20x/13

(E) 80x/9

Thanks in advance,

MS

MS,

machoman and others have already shown you very simple methods to solve this problem.

let me tell you a way to guess the answer, in case you forget the steps. ( I wish that this should not happen, but still....)

you know that X is sales from the Japanese things. Hence, Total sales would obviously greater than X. And, you need "billion dollars" as the unit so X should be in the numerator. This eliminates possibility of A, B, and C as the correct answer.

Now, 25% is 1/4th and 45% is 9/20. there is no 13 in the numbers anywhere. So, you can guess that D should not be the answer.

Pick the option that you are left with