To understand the problem consider the following cases.
i)
If we buy 1 packet of pencils, and 2 packet of erasers,
we have 1*10=10 pencils and 2*6=12 erasers.
ii)
If we buy 3 packet of pencils, and 4 packet of erasers,
we have 3*10=30 pencils and 4*6=24 erasers.
So let a and b be the correct number of packets of pencils and erasers respectively.
That is the least numbers a and b, such that 10a=6b.
10a=6b
divide both sides by 10:
[tex]a= \frac{6b}{10}= \frac{3b}{5}[/tex]
divide both sides by b:
[tex] \frac{a}{b} = \frac{3}{5} [/tex]
the ratio a:b cannot be simplified any further. This means that the smallest (natural) numbers a and b such that [tex] \frac{a}{b} = \frac{3}{5} [/tex] are a=3 and b=5
Answer:
3 packages of pencils, 5 packages of erasers.
