In 1985, the cost of clothing for a certain family was $620. In 1995, 10 years later, the cost of clothing for this family was $ 1,000. Assuming the cost increased linearly, what was the cost of this family's clothing in 1991?

Options

A. $908
B. $848
C. $812
D. $810

Answer

To find the cost of clothing for the family in 1991, we can follow these steps:

### Step 1: Identify the initial and final costs and the years.
- The cost of clothing in 1985 (initial year) = $620
- The cost of clothing in 1995 (final year) = $1000
- The time period from 1985 to 1995 = 10 years

### Step 2: Calculate the increase in cost over the years.
- Increase in cost = Cost in 1995 - Cost in 1985
- Increase in cost = $1000 - $620 = $380

### Step 3: Calculate the slope (rate of increase per year).
- Slope = Increase in cost / Number of years
- Slope = $380 / 10 = $38 per year

### Step 4: Write the formula for the cost of clothing in any year after 1985.
- Cost in year = Cost in 1985 + (Slope × Number of years since 1985)
- Cost in year = $620 + ($38 × y), where y is the number of years after 1985.

### Step 5: Determine the number of years since 1985 for the year 1991.
- For 1991, y = 1991 - 1985 = 6 years

### Step 6: Substitute y into the formula to find the cost in 1991.
- Cost in 1991 = $620 + ($38 × 6)
- Cost in 1991 = $620 + $228
- Cost in 1991 = $848

### Conclusion:
The cost of this family's clothing in 1991 was **$848**.

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