Question 02.
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.
$\begin{matrix} P a r t s o f r e d p i g m e n t & 1 & 4 & 7 & 12 & 20 P a r t s o f b a s e & 8 & \dots & \dots & \dots & \dots \end{matrix}$

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Solution

Let the ratio of parts of red pigment and parts of base be
$\frac{a}{b}$ .
$\begin{matrix} H e r e & a_{1} = 1, b_{1} = 8 & \Rightarrow & \frac{a_{1}}{b_{1}} = \frac{1}{8} = k (s a y) W h e n & a_{2} = 4, b_{2} = ? k = \frac{a_{2}}{b_{2}} & \Rightarrow & b_{2} = \frac{a_{2}}{k} = \frac{4}{\frac{1}{8}} = 4 \times 8 = 32 W h e n & a_{3} = 7, b_{3} = ? k = \frac{a_{3}}{b_{3}} & \Rightarrow & b_{3} = \frac{a_{3}}{k} = \frac{7}{\frac{1}{8}} = 7 \times 8 = 56 W h e n & a_{4} = 12, b_{4} = ? k = \frac{a_{4}}{b_{4}} & \Rightarrow & b_{4} = \frac{a_{4}}{k} = \frac{12}{\frac{1}{8}} = 12 \times 8 = 96 W h e n & a_{5} = 20, b_{5} = ? k = \frac{a_{5}}{b_{5}} & \Rightarrow & b_{5} = \frac{a_{5}}{k} = \frac{20}{\frac{1}{8}} = 20 \times 8 = 160 \end{matrix}$

$\begin{matrix} P a r t s o f r e d p i g m e n t & 1 & 4 & 7 & 12 & 20 P a r t s o f b a s e & 8 & 32 & 56 & 96 & 160 \end{matrix}$

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Question 02. 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. Parts of red pigment1471220Parts of base8…………