a worker makes 30000 a year. after 1 year he gets a raise of 5%. the next year he gets a raise of 10%. If he received no raise the first year, what percent increase would give him the same salary as consecutive raises of 5% and 10%?
would it be 50%
Nope! A 50% increase would give him a salary of $45,000.
30,000 * 1.05 = 31,500
31,500 * 1.1 = 34,650
34,650 - 30,000 = 4650
4,650/30,000 = 0.155 = 15.5%
what number is between 0.1 and 0.24
To find the percentage increase that would give the worker the same salary as consecutive raises of 5% and 10%, we need to break the problem down into smaller steps.
Step 1: Calculate the salary after the first raise of 5%
To get the salary after the first raise of 5%, we multiply the current salary by (1 + 0.05):
Salary after first raise = $30,000 * (1 + 0.05) = $31,500
Step 2: Calculate the salary after the second raise of 10%
To get the salary after the second raise of 10%, we multiply the salary after the first raise by (1 + 0.10):
Salary after second raise = $31,500 * (1 + 0.10) = $34,650
Step 3: Calculate the percentage increase needed to reach $34,650 from the initial salary of $30,000
To find the percentage increase, we use the following formula:
Percentage increase = (Final amount - Initial amount) / Initial amount * 100
Percentage increase = ($34,650 - $30,000) / $30,000 * 100 = $4,650 / $30,000 * 100 ≈ 15.5%
Therefore, to achieve the same salary as consecutive raises of 5% and 10%, the worker would need a percentage increase of approximately 15.5%.