Solved on Jan 21, 2024

Find the original salary before a 9% raise, given the current salary of $50,031.

STEP 1

Assumptions
1. The current salary is $50,031.00.
2. The raise received last year was 9%.

STEP 2

To find the salary before the raise, we need to consider the current salary as the result of a 9% increase on the previous year's salary. Let's denote the previous year's salary as $S$ .

STEP 3

The current salary can be expressed as the previous year's salary plus the raise, which is 9% of the previous year's salary.
$Current\, salary = S + (9\% \times S)$

STEP 4

Convert the percentage to a decimal value.
$9\% = 0.09$

STEP 5

Rewrite the equation using the decimal value for the percentage.
$\$50,031.00 = S + (0.09 \times S)$

STEP 6

Factor out $S$ from the right side of the equation to simplify.
$\$50,031.00 = S(1 + 0.09)$

STEP 7

Calculate the factor that represents the total percentage of the previous year's salary after the raise.
$1 + 0.09 = 1.09$

STEP 8

Rewrite the equation with the calculated factor.
$\$50,031.00 = S \times 1.09$

STEP 9

Now, solve for $S$ by dividing both sides of the equation by 1.09.
$S = \frac{\$50,031.00}{1.09}$

STEP 10

Perform the division to find the previous year's salary.
$S = \frac{\$50,031.00}{1.09} \approx \$45,899.08$
The salary last year before the raise was approximately $45,899.08.

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Find the original salary before a 9% raise, given the current salary of $50,031.

STEP 1

Assumptions
1. The current salary is $50,031.00.
2. The raise received last year was 9%.

STEP 2

To find the salary before the raise, we need to consider the current salary as the result of a 9% increase on the previous year's salary. Let's denote the previous year's salary as $S$ .

STEP 3

The current salary can be expressed as the previous year's salary plus the raise, which is 9% of the previous year's salary.
$Current\, salary = S + (9\% \times S)$

STEP 4

Convert the percentage to a decimal value.
$9\% = 0.09$

STEP 5

Rewrite the equation using the decimal value for the percentage.
$\$50,031.00 = S + (0.09 \times S)$

STEP 6

Factor out $S$ from the right side of the equation to simplify.
$\$50,031.00 = S(1 + 0.09)$

STEP 7

Calculate the factor that represents the total percentage of the previous year's salary after the raise.
$1 + 0.09 = 1.09$

STEP 8

Rewrite the equation with the calculated factor.
$\$50,031.00 = S \times 1.09$

STEP 9

Now, solve for $S$ by dividing both sides of the equation by 1.09.
$S = \frac{\$50,031.00}{1.09}$

STEP 10

Perform the division to find the previous year's salary.
$S = \frac{\$50,031.00}{1.09} \approx \$45,899.08$
The salary last year before the raise was approximately $45,899.08.

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Find the original salary before a 9% raise, given the current salary of $50,031.

STEP 1

Assumptions1. The current salary is $50,031.00.2. The raise received last year was 9%.

STEP 2

To find the salary before the raise, we need to consider the current salary as the result of a 9% increase on the previous year's salary. Let's denote the previous year's salary as SSS.

STEP 3

The current salary can be expressed as the previous year's salary plus the raise, which is 9% of the previous year's salary.Current salary=S+(9%×S)Current\, salary = S + (9\% \times S)Currentsalary=S+(9%×S)

STEP 4

Convert the percentage to a decimal value.9%=0.099\% = 0.099%=0.09

STEP 5

Rewrite the equation using the decimal value for the percentage.$50,031.00=S+(0.09×S)\$50,031.00 = S + (0.09 \times S)$50,031.00=S+(0.09×S)

STEP 6

Factor out SSS from the right side of the equation to simplify.$50,031.00=S(1+0.09)\$50,031.00 = S(1 + 0.09)$50,031.00=S(1+0.09)

STEP 7

Calculate the factor that represents the total percentage of the previous year's salary after the raise.1+0.09=1.091 + 0.09 = 1.091+0.09=1.09

STEP 8

Rewrite the equation with the calculated factor.$50,031.00=S×1.09\$50,031.00 = S \times 1.09$50,031.00=S×1.09

STEP 9

Now, solve for SSS by dividing both sides of the equation by 1.09.S=$50,031.001.09S = \frac{\$50,031.00}{1.09}S=1.09$50,031.00​

STEP 10

Perform the division to find the previous year's salary.S=$50,031.001.09≈$45,899.08S = \frac{\$50,031.00}{1.09} \approx \$45,899.08S=1.09$50,031.00​≈$45,899.08The salary last year before the raise was approximately $45,899.08.

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Assumptions
1. The current salary is $50,031.00.
2. The raise received last year was 9%.

To find the salary before the raise, we need to consider the current salary as the result of a 9% increase on the previous year's salary. Let's denote the previous year's salary as $S$ .

The current salary can be expressed as the previous year's salary plus the raise, which is 9% of the previous year's salary.
$Current\, salary = S + (9\% \times S)$

Convert the percentage to a decimal value.
$9\% = 0.09$

Rewrite the equation using the decimal value for the percentage.
$\$50,031.00 = S + (0.09 \times S)$

Factor out $S$ from the right side of the equation to simplify.
$\$50,031.00 = S(1 + 0.09)$

Calculate the factor that represents the total percentage of the previous year's salary after the raise.
$1 + 0.09 = 1.09$

Rewrite the equation with the calculated factor.
$\$50,031.00 = S \times 1.09$

Now, solve for $S$ by dividing both sides of the equation by 1.09.
$S = \frac{\$50,031.00}{1.09}$

Perform the division to find the previous year's salary.
$S = \frac{\$50,031.00}{1.09} \approx \$45,899.08$
The salary last year before the raise was approximately $45,899.08.