SOLUTION: In a bookshop, 40% of the stationery were pencils and the rest were erasers and rulers. The number of rulers is 1/4 the number of erasers. There were 120 more erasers than pencil

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a bookshop, 40% of the stationery were pencils and the rest were erasers and rulers. The number of rulers is 1/4 the number of erasers. There were 120 more erasers than pencil      Log On


   

Question 1209314: In a bookshop, 40% of the stationery were pencils and the rest were erasers and rulers. The number of rulers is 1/4
the number of erasers. There were 120 more erasers than pencils.
(a) What percentage of the stationery were erasers?
(b) How many rulers were there?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52847) About Me  (Show Source):
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In a bookshop, 40% of the stationery were pencils and the rest were erasers and rulers.
The number of rulers is 1/4 the number of erasers. There were 120 more erasers than pencils.
(a) What percentage of the stationery were erasers?
(b) How many rulers were there?
~~~~~~~~~~~~~~~~~~~~~ 

Let the number of rulers be x.
Then the number of erasers is 4x.


x + 4x = 5x is 60% of stationery;

hence, the number of pencils, which is 40% of stationery, is 2/3 of 5x,  or  %282%2F3%29%2A5x.


The problem says that there were 120 more erasers than pencils.

    4x - %282%2F3%29%2A5x = 120.


To solve it, multiply all the terms by 3

    12x - 10x = 3*120

        2x    =  360

         x    =   360/2 = 180.


So, the number of rulers was 180;  the number of erasers was 4x = 4*180 = 720;

    the number of pencils was %282%2F3%29%2A5x = %282%2F3%29%2A5%2A180 = 2*5*60 = 600.

Total stationery items was  180 + 720 + 600 = 1500.


(a)  Percentage of erasers to the total stationery was  %28720%2F1500%29%2A100 = 48%.    ANSWER


(b)  The number of rules was 180.    ANSWER

Solved.



Answer by josgarithmetic(39625) About Me  (Show Source):
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The pencils are 40% of the items, so the erasers and rulers together are 60% of the items.

The number of rulers is 1/4 the number of erasers, so
let 4x = percentage of items that are erasers
then x = percentage that are rulers

The erasers and rulers together are 60%:

4x+x = 60%
5x = 60%
x = 12%
4x = 48%

x = 12% of the items are rulers; 4x = 48% are erasers

ANSWER (a): 48% are erasers

The number of erasers is 120 more than the number of pencils.

48% are erasers; 40% are pencils. So the difference of 120 represents 48-40 = 8% of the total number of items. The total number of items is 120/.08 = 1500.

The rulers are 12% of the total number of items: .12(1500) = 180.

ANSWER (b) the number of rulers is 180