QuestionYou earn \$6,875. After a 6.5% pay cut, how much will your salary decrease? What will your new salary be? After a raise, will you return to your original salary?

Studdy Solution

STEP 1

Assumptions1. The original monthly salary is $6,875. The pay cut is6.5%
3. The pay raise is also6.5%
4. The pay cut and pay raise are calculated based on the current salary, not the original salary5. The results are rounded to the nearest cent

STEP 2

First, we need to find the amount of the pay cut. We can do this by multiplying the original salary by the pay cut percentage.
$Pay\, cut = Original\, salary \\times Pay\, cut\, percentage$

STEP 3

Now, plug in the given values for the original salary and pay cut percentage to calculate the pay cut.
$Pay\, cut = \$6,875 \\times6.5\%$

STEP 4

Convert the percentage to a decimal value.
$6.\% =0.065$ $Pay\, cut = \$6,875 \\times0.065$

STEP 5

Calculate the pay cut amount.
$Pay\, cut = \$,875 \\times0.065 = \$446.88$

STEP 6

Now that we have the pay cut amount, we can find the reduced salary. This is the original salary minus the pay cut.
$Reduced\, salary = Original\, salary - Pay\, cut$

STEP 7

Plug in the values for the original salary and the pay cut to calculate the reduced salary.
$Reduced\, salary = \$6,875 - \$446.88$

STEP 8

Calculate the reduced salary.
$Reduced\, salary = \$6,875 - \$446.88 = \$6,428.12$

STEP 9

Now, we need to find the amount of the pay raise. We can do this by multiplying the reduced salary by the pay raise percentage.
$Pay\, raise = Reduced\, salary \\times Pay\, raise\, percentage$

STEP 10

Plug in the given values for the reduced salary and pay raise percentage to calculate the pay raise.
$Pay\, raise = \$6,428.12 \\times6.5\%$

STEP 11

Calculate the pay raise amount.
$Pay\, raise = \$6,428. \\times0.065 = \$417.83$

STEP 12

Now that we have the pay raise amount, we can find the new salary. This is the reduced salary plus the pay raise.
$New\, salary = Reduced\, salary + Pay\, raise$

STEP 13

Plug in the values for the reduced salary and the pay raise to calculate the new salary.
$New\, salary = \$6,428.12 + \$417.83$

STEP 14

Calculate the new salary.
$New\, salary = \$6,428.12 + \$417.83 = \$6,845.95$

STEP 15

Finally, we compare the new salary to the original salary to see if they are equal. If they are not equal, we calculate the difference.
$Difference = Original\, salary - New\, salary$

STEP 16

Plug in the values for the original salary and the new salary to calculate the difference.
$Difference = \$6,875 - \$6,845.95$

STEP 17

Calculate the difference.
$Difference = \$6,875 - \$6,845.95 = \$29.05$ The new salary is $29.05 less than the original salary. Therefore, the employer's plan to reduce the salary by6.5% and then increase it by6.5% does not make the new monthly salary equal to the original monthly salary again.

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