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increase and descrease

Staples pays George Nagovsky an annual salary of $40,000. Today, George’s boss informs him that he will receive a $4,300 raise. What percent of George’s old salary is the $4,300 raise? (Round to the nearest tenth percent. Omit the "%" sign in your response.)

Comments

not quite sure what new problem means, do you still need this one answered? If so...

I like to think of the wording "is" being the numerator, and "of" being the denominator. And whenever you have a percent questions you set this is/of = percent/100

What percent:  x  (because we don't know this yet)

of George's old salary:  40,000

is the raise: 4,300

  4,300   =     x    

 40,000        100

Cross multiply

(40,000)x = (4,300)(100)

40,000x = 430,000

Divide by 40,000

40,000x = 430,000

40,000       40,000

x = 10.75%

I like Nicole's answer. In the original problem is the instruction "Round to the nearest tenth percent. Omit the "%" sign in your response."

To round Nicole's answer to the nearest percent, look at the first digit past the decimal point. If it is 5 or greater, then increase the one's digit. If it is 4 or less, then keep the one's digit the same. In this problem, we have:

10.75%

The first digit smaller than the % or one's place is the 7. It is greater than 5, so we round the one's digit up one. To the nearest %, we have 11%.

The other part of the instruction, "Omit the "%" sign in your response," is not clear to me. It could be that they want the answer to look like this:

11

instead of "11%"

I think it might be more likely that they want this percent displayed as a decimal. To covert a percent to a decimal, divide by 100.

11% as a decimal: 11/100 = 0.11

Again, I am not sure if this is what the instructions are asking. Perhaps you can tell from an example problem in the section you are working on.

Unfortunately, I cannot edit my comment, but I see that I made a mistake. To the nearest tenth, 10.75% rounds to 10.8%, not the answer I provided in my comment (11%).

So in decimal form, 10.8% is 0.108.

Sorry about the mixup.

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3 Answers

To find the increased mileage Maria will get with her new tires:


Step 1: Find 9% of 18 -> 18 X .09 = 1.62


Step 2: Add the percentage to the original miles -> 18 + 1.62 = 19.62 mpg

Before I address your specific question, I want to give a few tips on understanding word problems with percentages...

The word "of" means multiplication

The word "is" means equals

Percent means move the decimal two places to the left

Increase means 1 + the percentage as a decimal

 

With these tips in mind, I will try to walk you through this problem

If we begin by changing the percentage to a decimal, we have:

9% = .09

Because we are looking at an increase, we will add 1 to the decimal equivalent of the fraction.

1 + .09 = 1.09

We are now wanting to learn what a 9% increase "of" 18 mpg "is".

1.09 X 18 = 19.6 mpg

 

After = 9% better

9% better than what?

   It means 9% better than the before amount

To find 9% of th before amount of 18 mpg

  9% = 0.09

  (0.09)(18 mpg) = 1.62 mpg

If it is better than we need to add this amount to the before amount

  After = 18 + 1.62 = 19.62 mpg

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