Question

to estimate 103% of 63, rich rounded 103% down to 100%, 63 down to 60, and multiplied 60 by 1 to get 60. which of these statements is correct?
○ rich’s estimate is reasonable because it should be less than 63.
○ rich’s estimate is unreasonable because it should be exactly 63.
○ rich’s estimate is unreasonable because it should be less than 63.
○ rich’s estimate is reasonable because it should be greater than 63.

Explanation:

Step1: Understand the problem

We need to determine if Rich's estimate of 103% of 63 (by rounding 103% to 100% and 63 to 60, then multiplying 60 by 1 to get 60) is reasonable. First, recall that 100% of a number is the number itself, and 103% is more than 100%. So 103% of 63 should be more than 63 (since 103% > 100%, so 1.03×63 > 63).

Step2: Analyze each option

• Option 1: Says estimate is reasonable because it should be less than 63. But 103% of 63 is more than 63, so this is wrong.
• Option 2: Says estimate is unreasonable because it should be exactly 63. 103% of 63 is 1.03×63 = 64.89, not exactly 63, but the reason here is incorrect as it's not about being exactly 63.
• Option 3: Says estimate is unreasonable because it should be less than 63. But 103% of 63 is more than 63, so this is wrong.
• Option 4: Says estimate is unreasonable because it should be greater than 63. Since 103% > 100%, 103% of 63 is 1.03×63 = 64.89, which is greater than 63. Rich's estimate was 60, which is less than 63, so his estimate is unreasonable because the actual value should be greater than 63.

Answer:

The correct option is the fourth one: Rich's estimate is unreasonable because it should be greater than 63.