Question

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.
If 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

$\begin{array}{cccccc}Partsofredpigment& 1& 4& 7& 12& 20\\ Partsofbase& 8& & & & \end{array}$ [3 MARKS]

Answer 1

Table completion: 1.5 Marks
Answer for red pigment mix: 1.5 Marks

$k=\frac{x_1}{y_1}=\frac{1}{8}$

That is $y_1=x_1\times 8$

$y_2=4\times 8=32$

$y_3=7\times 8=56$

$y_4=12\times 8=96$

$y_5=20\times 8=160$

$\begin{array}{cccccc}Partsofredpigment& 1& 4& 7& 12& 20\\ Partsofbase& 8& 32& 56& 96& 160\end{array}$

Calculation of amount of red pigment required:

$x_1=1$ and $y_1=75$

$x_2=?$ and $y_2=1800$

$\frac{x_1}{y_1}=\frac{x_2}{y_2}$

$\frac{1}{75}=\frac{x_2}{1800}$

$x_2=\frac{1800}{75}=24$