Mathematical statement: Let's assume the original wage per hour is W.
Claim: Working 10 fewer hours at the same wage will result in earning more money.
According to the claim, the new earnings will be equal to the original earnings plus the earnings from the 10 fewer hours worked.
Original earnings = W * H (where H is the total hours worked originally)
New earnings = W * (H - 10)
To evaluate the reasonableness of the claim, we need to compare the new earnings to the original earnings.
Using the Commutative Property of Multiplication, we can rearrange the terms in the new earnings expression:
New earnings = (H - 10) * W
Using the Associative Property of Multiplication, we can further rearrange the terms:
New earnings = H * W - 10 * W
Now, comparing the original earnings to the new earnings:
New earnings - Original earnings = (H * W - 10 * W) - (W * H)
= H * W - 10 * W - W * H
Here, we can see that the terms -10 * W and -W * H are subtracted from the original earnings. Since the wage per hour is W, these terms are negative, and subtracting negative values will result in addition. Therefore, the expression can be simplified as:
New earnings - Original earnings = H * W - 10 * W - W * H
= 0
Hence, the claim of making more money by working 10 fewer hours at the same wage is not reasonable. The new earnings, according to the mathematical statement, are the same as the original earnings. Therefore, the advertisement's claim is not accurate.
“Get rich quick! Do you want to work fewer hours for the same amount of money per hour, and get even richer? Click here to see how you can relax and earn. You’ll work 10 fewer hours at the same wage, and you’ll still make more money!”
Represent the advertisement’s claim with a sample mathematical statement.
Using the Associative and Commutative Properties of Multiplication, evaluate whether the claim is reasonable.
Explain your reasoning in your post.
5 answers
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