Question

Cindy worked for 15 consecutive days, earning an average wage of $91 per day. During the first 7 days her average was $87/day, and her average during the last 7 days was $93/day. What was her wage on the 8th day?

A. $83 B. $92 C. $97 D. $105

(I believe it's D. But feel free to correct me if i'm wrong)

Answer 1

D. $105

Explanation:

Use definition:

`\text{Average of }n\text{ numbers}=\frac{\text{The sum of }n\text{ numbers}}{n}`

The average wage for 15 consecutive days is $91, then by definition

`\$91=\frac{\text{The sum of wages for 15 days}}{15}\Rightarrow \\ \\\text{The sum of wages for 15 days}=\$91\cdot 15=\$1,365`

The average wage for first 7 consecutive days is $87, then by definition

`\$87=\frac{\text{The sum of wages for first 7 days}}{7}\Rightarrow \\ \\\text{The sum of wages for first 7 days}=\$87\cdot 7=\$609`

The average wage for last 7 consecutive days is $93, then by definition

`\$93=\frac{\text{The sum of wages for last 7 days}}{7}\Rightarrow \\ \\\text{The sum of wages for last 7 days}=\$93\cdot 7=\$651`

Now,

`\text{The sum of wages for 15 days}=\text{The sum of wages for first 7 days }+\\ \\+\text{ The wage for 8th day}+\text{The sum of wages for last 7 days}\\ \\\$1,365=\$609+\text{ The wage for 8th day}+\$651\\ \\\text{ The wage for 8th day}=\$1,365-\$609-\$651=\$105`