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

[5 Marks]

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Solution

Let the ratio of the parts of red pigment and the parts of base be $\frac{a}{b}$ .
So, according to direct proportion,
$\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}} = \frac{a_{4}}{b_{4}} = \frac{a_{5}}{b_{5}}$

[1 Mark]

Let $\frac{a_{1}}{b_{1}} = \frac{1}{8}$ , $a_{2}$ = 4 and $b_{2}$ be its respective parts of base and so on.
$∴$ $\frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}} = \frac{a_{4}}{b_{4}} = \frac{a_{5}}{b_{5}} = \frac{1}{8}$
$\frac{a_{2}}{b_{2}} = \frac{4}{b_{2}} = \frac{1}{8}$
$\Rightarrow b_{2} = 32$

[1 Mark]

$\frac{a_{3}}{b_{3}} = \frac{7}{b_{3}} = \frac{1}{8}$
$\Rightarrow b_{3} = 56$

[1 Mark]

$\frac{a_{4}}{b_{4}} = \frac{12}{b_{4}} = \frac{1}{8}$
$\Rightarrow b_{4} = 96$

[1 Mark]

$\frac{a_{5}}{b_{5}} = \frac{20}{b_{5}} = \frac{1}{8}$
$\Rightarrow b_{5} = 160$

[1 Mark]

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A mixture of paint is prepared by mixing 1 part of red pigment with 8 parts of base. In the following table, find the parts of base that need to be added for the respective parts of red pigment. [5 Marks]

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

[5 Marks]