Math

QuestionYou have a job with a monthly salary of \$6,975. After a 6.5% pay cut, how much will your salary decrease?
(a) Calculate the decrease in dollars.
(b) What will your new salary be after the cut?
(c) If you get a 6.5% raise after that, how much will your salary increase?

Studdy Solution

STEP 1

Assumptions1. The original monthly salary is $6,975. The pay cut rate is6.5%
3. The pay cut is applied to the original monthly salary4. The pay cut is a one-time deduction, not a recurring monthly deduction5. The pay raise rate is also6.5%
6. The pay raise is applied to the reduced monthly salary7. The pay raise is a one-time addition, not a recurring monthly addition

STEP 2

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

STEP 3

Now, plug in the given values for the original monthly salary and pay cut rate to calculate the pay cut.
Paycut=$6,975times6.5%Pay\, cut = \$6,975 \\times6.5\%

STEP 4

Convert the percentage to a decimal value.
6.%=0.0656.\% =0.065Paycut=$6,975times0.065Pay\, cut = \$6,975 \\times0.065

STEP 5

Calculate the pay cut amount.
Paycut=$,975times0.065=$453.38Pay\, cut = \$,975 \\times0.065 = \$453.38

STEP 6

Now that we have the pay cut amount, we can find the reduced monthly salary. This can be done by subtracting the pay cut from the original monthly salary.
Reducedmonthlysalary=OriginalmonthlysalaryPaycutReduced\, monthly\, salary = Original\, monthly\, salary - Pay\, cut

STEP 7

Plug in the values for the original monthly salary and the pay cut to calculate the reduced monthly salary.
Reducedmonthlysalary=$6,975$453.38Reduced\, monthly\, salary = \$6,975 - \$453.38

STEP 8

Calculate the reduced monthly salary.
Reducedmonthlysalary=$6,975$453.38=$6,521.62Reduced\, monthly\, salary = \$6,975 - \$453.38 = \$6,521.62

STEP 9

Next, we need to find the amount of the pay raise. We can do this by multiplying the reduced monthly salary by the pay raise rate.
Payraise=ReducedmonthlysalarytimesPayraiseratePay\, raise = Reduced\, monthly\, salary \\times Pay\, raise\, rate

STEP 10

Now, plug in the given values for the reduced monthly salary and pay raise rate to calculate the pay raise.
Payraise=$6,521.62times6.5%Pay\, raise = \$6,521.62 \\times6.5\%

STEP 11

Calculate the pay raise amount.
Payraise=$6,521.62times0.065=$423.91Pay\, raise = \$6,521.62 \\times0.065 = \$423.91The monthly pay will increase by approximately $423.91.

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