# Ratios: Pencils and Notebooks

#### sigma

Suppose p:n = 9:4 then after p-10=n or p=n+10, the ratio 9/4 turns into 4:4
what are the end values of p and n?

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#### skipjack

Forum Staff

Using p for the number of pencils and n for the number of notebooks, p/n = 9/4 and p - 10 = n.

The first equation implies p = 9n/4, and replacing p with 9n/4 in the second equation gives 9n/4 - 10 = n.

Hence n = 10/(9/4 - 1) = 8, and so p = 9(8/4) = 18.

After 10 pencils are sold, p becomes 8, making p and n each equal 8.

The ratio 8:8 is equal to 4:4 (though that could be simplified to 1:1).

#### greg1313

Forum Staff
$$\frac{p}{n}=\frac{9}{4}$$

$$4p=9n$$

$$4p=9(p-10)\Leftarrow n=p-10$$

$$4p=9p-90$$

$$90=5p$$

$$p=18$$

$$\text{end }n=8,\,\text{end }p=8$$