Last night's six inches of snow brings the month's total to fifty-eight inches. Men's jacket sizes are 36-inch, 38-inch, 40-inch, 42-inch, and 44-inch. Her starting salary was $34,... Last night's six inches of snow brings the month's total to fifty-eight inches. Men's jacket sizes are 36-inch, 38-inch, 40-inch, 42-inch, and 44-inch. Her starting salary was $34,000, but each year she received a $1,000 raise until she was earning $40,000 a year.
Understand the Problem
The question presents a series of statements related to incremental changes: one regarding snowfall, another about jacket sizes, and a third about salary increments. It appears to seek an understanding of how each example illustrates the concept of increments.
Answer
The previous snowfall was 52 inches, each jacket size increases by 2 inches, and it took her 6 years to reach a salary of $40,000.
Answer for screen readers
- Previous snowfall total was 52 inches.
- Each men's jacket size has an increment of 2 inches.
- It took her 6 years to reach a salary of $40,000.
Steps to Solve
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Understand the Increment in Snowfall
Last night, 6 inches of snow was added to the existing total. The previous total can be calculated as: $$ 58 \text{ inches (current total)} - 6 \text{ inches (new snowfall)} = 52 \text{ inches (previous total)} $$
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Identify Increment in Jacket Sizes
The sizes of men's jackets given are 36 inches, 38 inches, 40 inches, 42 inches, and 44 inches. The incremental change between each size can be represented as: $$ 38 - 36 = 2, \quad 40 - 38 = 2, \quad 42 - 40 = 2, \quad 44 - 42 = 2 $$ Each jacket size increases by 2 inches.
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Calculate Salary Increments
Starting with a salary of $34,000, she received a $1,000 raise each year. To find out in how many years she reached $40,000, we can set up the equation: $$ 34,000 + 1,000n = 40,000 $$ Solving for $n$: $$ 1,000n = 40,000 - 34,000 $$ $$ 1,000n = 6,000 $$ $$ n = 6 $$
Thus, it took her 6 years to reach a salary of $40,000.
- Previous snowfall total was 52 inches.
- Each men's jacket size has an increment of 2 inches.
- It took her 6 years to reach a salary of $40,000.
More Information
These examples illustrate the idea of increments in various contexts: natural phenomena (snow), clothing sizes, and personal finance (salary). Each shows a clear and consistent increase over time or size.
Tips
- Forgetting to subtract the new snowfall to find the previous total.
- Miscalculating differences in jacket sizes by not recognizing the consistent increments.
- Overlooking how many years it takes to reach a final salary by misapplying the equation for salary calculation.
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