A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.

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Solution

While mixing, the ratio of pigment and base should be the same.

As parts of pigment will increase, the parts of base will also increase.

Hence, it is a case of direct proportion.

We have red pigment to base ratio given as $1 : 8$
Let part of base be $x$

(a) For red pigment equals to $4$ :

$\Rightarrow \frac{1}{8} = \frac{4}{x}$
$\Rightarrow x = 8 \times 4 = 32$

(b) For red pigment $= 7$ , :

$\Rightarrow \frac{1}{8} = \frac{7}{x}$
$\Rightarrow x = 8 \times 7 = 56$

(c) For red pigment $= 12$ :

$\Rightarrow \frac{1}{8} = \frac{12}{x}$
$\Rightarrow x = 8 \times 12 = 96$

(d) For red pigment $= 20$ :

$\Rightarrow \frac{1}{8} = \frac{20}{x}$
$\Rightarrow x = 8 \times 20 = 160$

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