Question

7. Eugene earns $2,700 monthly. He is going to be receiving a 3.5% raise. With this new raise, he

Inelieves he will earn more than $2,800 a month. Is Eugene correct in his thinking? Why or why
rot? Justify your reasoning.

Answer 1

Answer: No

Step-by-step explanation: to find out how much more money Eugene will be making we need to isolate the increased value provided by the raise and then add it to his already existing earnings. We do this by multiplying $2700 by 3.5%.

We would write this as 2700 x .035

This is because 100% can be converted to 1, for example if Eugene got a 100% raise we would multiply 2700 by 1 (which changes nothing) then add 2700 and 2700 together.

Since Eugene is only getting a 3.5% raise we would write it as .035 instead of 1

Now that we have our equation we first need to simplify. In this case it means we remove the two zero's from 2700 to make it 27. To make sure the answer does not get messed up will make the other side of the equation larger by moving everything two decimal points (one for each removed zero) like this.

27 x 3.5

This is much easier to work with but I will still show the steps I am using to prevent confusion.

27 x .5 = 13.5

27 x 3 = 20 x 3 + 7 x 3

20 x 3 = 60

7 x 3 =21

60+21 =81

81+13.5=94.5

Since 2700 + 94.5 = 2794.5 Eugene will not make more than $2800 dollars a month after his raise.

Answer 2

No, Eugene is not correct in his thinking. Even with a 3.5% raise, his monthly earnings would be $2,795.50, which is still below $2,800.

Step-by-step explanation:

Eugene's current monthly earnings are $2,700. To calculate his raise, we need to find 3.5% of $2,700. The formula for calculating a percentage increase is:

`\[ \text{New Value} = \text{Old Value} + (\text{Old Value} * \text{Percentage Increase}) \]`

In this case, Eugene's new monthly earnings (New Value) would be:

`\[ \$2,700 + (\$2,700 * 0.035) = \$2,795.50 \]`

So, with the 3.5% raise, Eugene's new monthly earnings would be $2,795.50, not exceeding $2,800.

Eugene's belief is incorrect because the raise is calculated on his existing salary, and the increase is not sufficient to surpass the $2,800 threshold. It's essential to accurately calculate percentage raises to understand the impact on income. In this scenario, Eugene's raise falls short of reaching the desired monthly earnings. It's crucial for individuals to verify their calculations to make informed assessments about their financial expectations.