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