Question

8 erika wants at least 6 kilograms of apples for a recipe. she picks a 2.56 - kilogram bag of red apples, a 1.18 - kilogram bag of green apples, and a 2.79 - kilogram bag of yellow apples. does erika need to pick more apples? use estimation only to decide. then explain if you are confident in your estimate or if you need to find an actual sum. show your work. erika to pick more apples.

Explanation:

Step1: Estimate each bag's weight

Round 2.56 to 2.6, 1.18 to 1.2, 2.79 to 2.8.

Step2: Sum the estimated weights

Calculate \(2.6 + 1.2 + 2.8\). First, \(2.6+1.2 = 3.8\), then \(3.8 + 2.8 = 6.6\) (wait, no, correction: 2.6 + 1.2 is 3.8, 3.8 + 2.8 is 6.6? Wait, no, original numbers: 2.56, 1.18, 2.79. Wait, maybe better to round to nearest whole or tenths. Alternatively, round 2.56 to 2.6, 1.18 to 1.2, 2.79 to 2.8. Sum: 2.6 + 1.2 = 3.8; 3.8 + 2.8 = 6.6. But wait, actual sum: 2.56 + 1.18 = 3.74; 3.74 + 2.79 = 6.53. Wait, but the estimation here: if we round down, 2.56 to 2.5, 1.18 to 1.1, 2.79 to 2.7. Then sum: 2.5 + 1.1 = 3.6; 3.6 + 2.7 = 6.3. Still more than 6. Wait, but the problem says "at least 6". Wait, maybe my initial rounding was up. Wait, the question is to estimate. Let's do conservative estimation: round each to the nearest lower tenth. 2.56 → 2.5, 1.18 → 1.1, 2.79 → 2.7. Sum: 2.5 + 1.1 = 3.6; 3.6 + 2.7 = 6.3. Since 6.3 ≥ 6, but wait, actual sum is 2.56 + 1.18 + 2.79 = 6.53. Wait, but the estimation: if we round each number down, the sum is 6.3, which is more than 6. So even with conservative estimation (rounding down), the sum is more than 6? Wait, no, 2.56 is 2.56, which is more than 2.5; 1.18 more than 1.1; 2.79 more than 2.7. So the actual sum is more than 6.3, which is more than 6. Wait, but maybe I made a mistake. Wait, let's recalculate the estimated sum correctly. Let's use rounding to the nearest whole number: 2.56 ≈ 3, 1.18 ≈ 1, 2.79 ≈ 3. Sum: 3 + 1 + 3 = 7, which is more than 6. Or rounding to tenths: 2.6 + 1.2 + 2.8 = 6.6. Either way, the estimated sum is at least 6.3 (conservative) or higher. Wait, but the problem says "at least 6". So if the estimated sum (even when rounding down) is more than 6, then she has enough? Wait, no, wait the question is "Does Erika need to pick more apples?" So if her total is at least 6, she doesn't. But wait, let's check the actual sum: 2.56 + 1.18 = 3.74; 3.74 + 2.79 = 6.53. So 6.53 ≥ 6, so she doesn't need to pick more. But with estimation: let's do it properly. Let's round each number to the nearest tenth: 2.56 ≈ 2.6, 1.18 ≈ 1.2, 2.79 ≈ 2.8. Sum: 2.6 + 1.2 = 3.8; 3.8 + 2.8 = 6.6. 6.6 ≥ 6, so the estimate shows she has at least 6 (since we rounded up, but even if we rounded down, 2.5 + 1.1 + 2.7 = 6.3 ≥ 6). So the estimate suggests she has enough, but to be precise, maybe check actual sum. But the question says use estimation only. So based on estimation, the sum is around 6.3 to 6.6, which is more than 6, so she does not need to pick more. Wait, but my initial miscalculation: wait 2.56 + 1.18 is 3.74, plus 2.79 is 6.53. So yes, more than 6. So with estimation, even rounding down, we get 6.3, which is more than 6, so she doesn't need to pick more.

Answer:

Erika does not need to pick more apples. (The estimation: rounding each weight to the nearest tenth: 2.6 + 1.2 + 2.8 = 6.6 (or rounding down: 2.5 + 1.1 + 2.7 = 6.3), both ≥ 6, so she has enough. To be confident, the actual sum is 6.53, but estimation shows it's at least 6.3, so she doesn't need more.)