Look at this estimate of the cost of a bag of pears that weighs 6.78 pounds.
[tex]$1.41(6.78) \approx $1 \times 7=$7[/tex]
Which statements are true about the estimate? Check all that apply.
A. The estimate is correct.
B. The estimate is incorrect.
C. The exact product is less than $7.
D. The exact product is greater than $7.
Answer (2)
The estimate provided for the cost of the pears is incorrect because the exact cost is approximately 9.56 , which is greater than $7. Therefore, the true statements are that the estimate is incorrect and the exact product is greater than $7.
;
Calculate the exact product: 1.41 × 6.78 = 9.5598 .
Compare the exact product with the estimate: 9.5598 = 7 , so the estimate is incorrect.
Compare the exact product with $7: 7"> 9.5598 > 7 , so the exact product is greater than 7 .
The estimate is incorrect and the exact product is greater than 7 , so the final answer is T h ees t ima t e i s in correc t . T h ee x a c tp ro d u c t i s g re a t er t han $7.
Explanation
Understanding the Problem We are given an estimate of the cost of a bag of pears that weighs 6.78 pounds: $1.41(6.78) \approx $1 \times 7 = 7 . We need to determine if the estimate is correct, and whether the exact product is less than or greater than $7.
Calculating the Exact Product First, let's calculate the exact product of 1.41 and 6.78.
Exact Product The exact product of 1.41 and 6.78 is 1.41 × 6.78 = 9.5598 .
Comparing with the Estimate Now, let's compare the exact product with the estimate of $7. The estimate is $7, and the exact product is $9.5598. Since 9.5598 = 7 , the estimate is incorrect.
Comparing with $7 Next, let's compare the exact product with $7 to determine if the exact product is less than or greater than $7. Since 7"> 9.5598 > 7 , the exact product is greater than $7.
Conclusion Therefore, the estimate is incorrect, and the exact product is greater than $7.
Examples
Estimating costs is a common practice in everyday life. For example, when grocery shopping, you might estimate the total cost of your items to ensure you stay within budget. If you're buying 6.78 pounds of apples at $1.41 per pound, you can quickly estimate the cost by rounding the weight to 7 pounds and the price to $1 per pound, giving you an estimate of $7. This helps you quickly gauge if you have enough money or if you need to adjust your purchases.
