Cherries cost $5.68 a pound. Will $20 be enough to buy a 4.1-pound bag of cherries?
Explain how to determine whether $20 is the correct estimate of the product of $5.68(4.1).
Answer (2)
$20 is not sufficient to purchase a 4.1-pound bag of cherries costing $5.68 per pound, as the total cost rounds to $23.29. An estimation round to $24 further confirms that the available budget is inadequate. Thus, $20 is an underestimate.
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Calculate the total cost: $5.68 \times 4.1 = $23.29.
Compare the total cost to the available money: $23.29 > $20, so $20 is not enough.
Estimate the product by rounding: 5.68 ≈ 6 and 4.1 ≈ 4 , so 6 × 4 = 24 .
Compare the estimate to the actual cost: $20 is an underestimate. The final answer is No.
Explanation
Calculate the Total Cost First, we need to determine the total cost of the cherries. To do this, we multiply the cost per pound by the number of pounds:
Calculating the Exact Cost The cost of cherries per pound is $5.68, and we are buying 4.1 pounds. So, the total cost is: 5.68 × 4.1 = 23.288 Rounding to the nearest cent, the total cost is $23.29.
Comparing Cost to Available Money Now, we compare the total cost to the amount of money we have, which is $20. Since $23.29 > $20, we do not have enough money to buy the cherries.
Estimating the Product Next, let's estimate the product of $5.68 and 4.1. We can round each number to the nearest whole number. $5.68 rounds to $6, and $4.1 rounds to $4.
Calculating the Estimate Multiplying the rounded numbers gives us an estimate: 6 × 4 = 24 So, our estimate is $24.
Evaluating the Estimate Finally, we compare our estimate of $24 to the given estimate of $20. Since the actual cost is $23.29, an estimate of $24 is closer to the actual cost than $20. Therefore, $20 is not a good estimate; it's an underestimate.
Final Answer In conclusion, $20 is not enough to buy the 4.1-pound bag of cherries, and $20 is not a good estimate of the product of $5.68 and 4.1.
Examples
Imagine you're planning a picnic and need to buy several items. You estimate the cost of each item and then multiply to find the total. This problem is similar, helping you determine if you have enough money for your purchase. Understanding how to estimate and calculate costs accurately ensures you don't run out of money during your shopping trip. It also teaches you to make informed decisions based on estimations and precise calculations.
