Last year a manufacturer had a sales total for January that was $50$ percent greater than the average(arithmetic mean) of the monthly sales totals for February through December. Calculate, the sales total for January was what fraction of the sales total for the year.

\frac{1}{11}

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\frac{1}{8}

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\frac{3}{25}

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\frac{3}{22}

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\frac{3}{5}

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Solution

The correct option is C $\frac{3}{25}$
Let the average monthly sales from February to December is $x$ .
Then total sales from February to December $=$ $11 \times x = 11 x$
Then total sale for January $=$ $\frac{150}{100} \times x = 1.5 x$ ( because January sale $50 %$ greater then average sale)
Then total sales January to December $=$ $11 x + 1.5 x$
So, fraction of January sales of total sales $=$ $\frac{1.5 x}{11 x + 1.5 x} = \frac{1.5 x}{12.5 x} = \frac{3}{25}$

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Last year a manufacturer had a sales total for January that was 50 percent greater than the average(arithmetic mean) of the monthly sales totals for February through December. Calculate, the sales total for January was what fraction of the sales total for the year.

Last year a manufacturer had a sales total for January that was $50$ percent greater than the average(arithmetic mean) of the monthly sales totals for February through December. Calculate, the sales total for January was what fraction of the sales total for the year.