   SEARCH HOME Math Central Quandaries & Queries  Question from Annette: If I sold a widget at $\$15.5017.5\%$of the time and$\$16.50$ $88.5\%$ of the time what is the algebraic expression for that. How do I arrive at an average price Hi Annette,

I think your 88.5% should be 83.5% since $17.5 + 83.5 = 100.$

I want to write the percentages as decimal fractions so $17.5\% = 0.175.$

Suppose you sold 100 widgets then you sold $100 \times 0.175 = 17.5$ items at $\$15.50$for a total of$\$15.50 \times 17.50.$ Likewise for the remaining widgets you receives $\$16.50 \times 83.50.$The total was on 100 widgets sold so the average price was $\frac{\15.50 \times 17.50 + \16.50 \times 83.50}{100}$ I didn't do the arithmetic as it is the form that is important not the answer. Suppose you sold$x$widgets then you sold$x \times 0.175$items at$\$15.50$ for a total of $\$15.50 \times 0.175 \times x.$Likewise for the remaining widgets you receives$\$16.50 \times 0.835 \times x.$ The total was on $x$ widgets sold so the average price was

$\frac{\15.50 \times 0.1750 \times x+ \16.50 \times 0.8350 \times x}{x} = \frac{\left(\15.50 \times 0.1750 + \16.50 \times 0.8350\right) \times x}{x} = \15.50 \times 0.1750 + \16.50 \times 0.8350$

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.