Last year a dinner cost $32 and a bottle of wine cost $18. This year the cost of the dinner increased by 5% and the cost of the wine increased by 10%. What was the percent increase in the combined cost of the dinner and wine?

It might be tempting to simply average the two percentage increases, but that would give you an incorrect result. The key is that the 5% and 10% increases are applied to different initial amounts. Because the dinner ($32) was a larger part of the original bill than the wine ($18), its percentage change has a greater "weight" on the final outcome. This concept is known as a weighted average, where some components influence the total more than others.

To find the correct answer, we must first work with the actual dollar amounts. The original total cost was $50 ($32 + $18). The 5% increase on the dinner adds $1.60, making it $33.60. The 10% increase on the wine adds $1.80, making it $19.80. The new combined cost is therefore $53.40. This means the total price went up by $3.40. To find the overall percentage increase, we divide this dollar change by the original total cost: $3.40 divided by $50 gives us the final result.

This type of calculation has important real-world applications. Economists use this exact principle to calculate inflation with the Consumer Price Index (CPI). They track price changes across a "basket" of common goods and services, from housing to groceries. Price hikes on major expenses like rent are weighted more heavily than those on smaller purchases, providing a more accurate picture of how inflation truly impacts the average person's cost of living.