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?

Understanding how individual price changes affect an overall cost requires a bit more than just averaging percentages. While the dinner increased by 5% and the wine by 10%, the final combined percentage increase isn't simply 7.5%. This is because the initial costs of the dinner and wine were different, meaning each item contributes a different proportion to the total expense. Last year, the dinner cost $32 and the wine cost $18, making the total $50.

To find this year's total, we first calculate the new individual prices. The dinner's 5% increase adds $1.60 ($32 x 0.05), making it $33.60. The wine's 10% increase adds $1.80 ($18 x 0.10), bringing its price to $19.80. Adding these new prices together, the combined cost for this year is $33.60 plus $19.80, which totals $53.40. Comparing this to last year's $50, the absolute increase is $3.40.

To express this as a percentage, we divide the total increase by the original total cost and multiply by 100. So, $3.40 divided by $50 equals 0.068. Multiplying by 100 gives us a 6.8% increase. This illustrates the concept of a weighted average, where the larger initial cost of the dinner had a greater influence on the overall percentage change, despite the wine having a higher individual percentage increase. Such calculations are crucial for budgeting, understanding inflation, or even assessing investment returns, as they reveal the true impact of varying price shifts on a total sum.