.
Lorraine bought some stationery. The ratio of pens to to pencils to erasers is 6 to 13 to 4 .
She then gave away some pencils and pens. The ratio of pens; pencils ; erasers left was 4 to 17 to 7.
If she had 91 pencils at first how many pens and pencils did she give away.
~~~~~~~~~~~~~~~~~~~
Originally, Lorraine had 6x pens, 13x pencils and 4x erasers.
After giving away some pencils and pens, she has 4y pens, 17y pencils and 7y erasers.
But the number of erasers didn't change; so, 4x = 7y erasers.
If she had 91 pencils originally, it means that 91 = 13x; hence x = 91/13 = 7;
so, originally Lorraine had 6*7 = 42 pencils; 13*7 = 91 pens and 4*7 = 28 erasers.
Next, 28 = 7y erasers means that y = 28/7 = 4.
It implies, that after giving away, there are 4*4 = 16 pencils and 17*4 = 68 pens.
Thus, the number of pens she gave away, was 91-68 = 23,
and the number of pencils she gave away, was 42-16 = 26.
ANSWER. Lorraine gave away 23 pens and 26 pencils.
Solved.
(