What is the average number of 6B-Pencils sold by stores A and E together?

Concept — In a ratio a : b the two quantities are multiples of one common unit. When one quantity and the ratio are known, divide that quantity by its own ratio number to get the value of a single unit, then multiply that unit by the other ratio number to get the second quantity. The average of n quantities is their sum divided by n.

Application — Only the two stores named in the question are used, and the column heading fixes the reading order as HB : 6B.

1. Store A sold 216 HB-pencils with HB : 6B = 9 : 5, so one ratio unit = 216 ÷ 9 = 24 pencils, and its 6B-pencil sale = 5 × 24 = 120.

2. Store E sold 240 HB-pencils with HB : 6B = 3 : 2, so one ratio unit = 240 ÷ 3 = 80 pencils, and its 6B-pencil sale = 2 × 80 = 160.

3. Combined 6B-pencil sale of the two stores = 120 + 160 = 280.

4. Average over the two stores = 280 ÷ 2 = 140 6B-pencils.

Cross-check — Rebuilding each ratio from the values obtained returns the table exactly: 216 : 120 = 9 : 5 for A and 240 : 160 = 3 : 2 for E. An average of two numbers must also lie between them, and 140 lies between 120 and 160.

Common pitfall — Reversing the ratio (multiplying by 9/5 or 3/2 instead of dividing) or averaging the HB figures instead of the derived 6B figures both change the result; the rows for B, C and D carry no information for this question.