Percentages, SM-Bank 045

John uses concrete in his landscaping business.

He makes a dry mix using 1 part cement, 2 parts sand and 3 parts gravel.

Express the amount of gravel as a fraction of the total mix. Give your answer in simplest form. (1 mark)
Express the amount of sand as a percentage of the total mix. (2 marks)
Express the amount of cement compared to the total mix. Give your answer as a recurring decimal. (2 marks)

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a. \(\dfrac{1}{2}\)

b. \(33\dfrac{1}{3}\%\)

c. \(0.1\dot{6}\)

Show Worked Solution

a. \(\text{Gravel as fraction of total}\)

\(=\dfrac{3}{6}=\dfrac{1}{2}\)

b. \(\text{Sand as percentage of total}\)

\(=\dfrac{2}{6}\times 100=\dfrac{1}{3}\times 100=33\dfrac{1}{3}\%\)

c. \(\text{Cement compared to total}\)

\(=\dfrac{1}{6}=0.16666\ldots\approx 0.1\dot{6}\)