The formula for the preceding exercise is a special case of the following formula for the weighted mean:

\[\bar{x}_{w}=\frac{\sum_{i=1}^{k} w_{i} x_{i}}{\sum_{i=1}^{k} w_{i}}\]

where $w_{i}$ is a weight indicating the relative importance of the $i$ th observation.

(a) If an instructor counts the final examination in a course four times as much as each 1-hour examination, what is the weighted average grade of a student who received grades of $69,75,56$, and 72 in four 1-hour examinations and a final examination grade of 78 ?

(b) From 2010 to 2015, the cost of food in a certain city increased by $60 %$, the cost of housing increased by $30 %$, and the cost of transportation increased by $40 %$. If the average salaried worker spent $24 %$ of his or her income on food, $33 %$ on housing, and $15 %$ on transportation, what is the combined percentage increase in the total cost of these items.