Question

mrs. garcia’s students were asked to find 220% of 75. each of the students had a different method. amy: “i multiplied 2.20 by 75 to find my answer.” braden: “i created a table with columns for 100%, 100%, 20%, and 220%. then i filled in the table and added the values.” colton: “i created a table with columns for 100%, 10%, 10%, and 220%. then i filled in the table and added the values.” danielle: “i divided 75 by 5 to find 20%. then i added 75 twice to what i found to get my final answer.” if all of the students completed their steps accurately, which student got the answer wrong? amy braden colton danielle

Explanation:

Step1: Calculate 220% of 75

To find a percentage of a number, we convert the percentage to a decimal (or fraction) and multiply. 220% as a decimal is 2.20. So, \( 2.20\times75 = 165 \).

Step2: Analyze Amy's method

Amy multiplied 2.20 by 75. \( 2.20\times75 = 165 \), so Amy is correct.

Step3: Analyze Braden's method

Braden used a table with 100%, 100%, 20% (since \( 100\% + 100\% + 20\% = 220\% \)).
- 100% of 75 is \( 1\times75 = 75 \)
- Another 100% of 75 is \( 1\times75 = 75 \)
- 20% of 75 is \( 0.2\times75 = 15 \)
- Adding them: \( 75 + 75 + 15 = 165 \), so Braden is correct.

Step4: Analyze Colton's method

Colton used a table with 100%, 10%, 10%, 220%? Wait, \( 100\% + 10\% + 10\% = 120\% \), not 220%. Wait, no, maybe misread. Wait, 220% can be broken down as 100% + 100% + 20% (as Braden) or 200% + 20% (which is 2\times100% + 20%). But Colton's breakdown: 100% + 10% + 10% + 220%? No, that doesn't make sense. Wait, no, let's recalculate. Wait, maybe Colton's table columns are 100%, 10%, 10%, and 220%? No, that's incorrect. Wait, no, 220% is 2.2 times the number. Let's check his addition. Wait, maybe I misread. Wait, the problem says Colton's table has columns for 100%, 10%, 10%, and 220%? No, that can't be. Wait, no, 100% + 10% + 10% = 120%, not 220%. Wait, maybe a typo, but let's check Danielle's method.

Step5: Analyze Danielle's method

Danielle divided 75 by 5 to find 20% (since \( 75\div5 = 15 \), which is 20% of 75, correct). Then she added 75 twice to what she found. Wait, 75 twice is \( 75 + 75 = 150 \), plus 15 is \( 150 + 15 = 165 \)? Wait, no, wait: "Then I added 75 twice to what I found". Wait, "what I found" is 15 (20% of 75). So \( 15 + 75 + 75 = 165 \)? Wait, that's correct. Wait, no, maybe I messed up Colton. Wait, let's re-express 220%: 220% = 200% + 20% = 2\times100% + 20%. So 200% of 75 is \( 2\times75 = 150 \), 20% of 75 is 15, so 150 + 15 = 165. Braden's breakdown: 100% + 100% + 20% = 220%, so 75 + 75 + 15 = 165. Amy: 2.2\times75 = 165. Danielle: 75/5 = 15 (20%), then added 75 twice: 15 + 75 + 75 = 165? Wait, no, 75 twice is 150, plus 15 is 165. Wait, but Colton's table: 100% (75) + 10% (7.5) + 10% (7.5) = 75 + 7.5 + 7.5 = 90, then plus 220%? No, that's not right. Wait, maybe Colton's table is incorrect. Wait, the question is which student got the answer wrong. Let's recalculate each:

- Amy: \( 2.20\times75 = 165 \) ✔️
- Braden: 100% (75) + 100% (75) + 20% (15) = 75 + 75 + 15 = 165 ✔️
- Colton: Let's see, 100% (75) + 10% (7.5) + 10% (7.5) = 75 + 7.5 + 7.5 = 90. Then where does 220% come in? His method is incorrect because the sum of 100% + 10% + 10% is 120%, not 220%. So his breakdown is wrong. Wait, but maybe I misread. Wait, the problem says "columns for 100%, 10%, 10%, and 220%". No, that can't be. Wait, maybe a mistake in the problem, but let's check Danielle. Danielle: 75 divided by 5 is 15 (20%), then added 75 twice: 15 + 75 + 75 = 165. Wait, that's correct. Wait, so Colton's method is wrong? Wait, no, maybe I made a mistake. Wait, 220% is 2.2, which is 2 + 0.2. 2 is 200% (2\times100%), 0.2 is 20%. So 200% + 20% = 220%. So Braden's breakdown (100% + 100% + 20%) is correct (200% + 20%). Colton's breakdown: 100% + 10% + 10% + 220%? No, that's adding 100% + 10% + 10% = 120%, then 220%? That's not how percentage breakdown works. So Colton's method is incorrect. Wait, but the options are Amy, Braden, Colton, Danielle. Wait, let's recalculate each:

- Amy: \( 2.2 \times 75 = 165 \) ✔️
- Braden: 100% (75) + 100% (75) + 20% (15) = 75 + 75 + 15 = 165 ✔️
- Colton: Let's see, if his table is 100%, 10%, 10%, and 220%, that's not a valid breakdown. Wait, maybe he meant 100% + 100% + 20% but wrote 10% + 10%? No, the problem says "columns for 100%, 10%, 10%, and 220%". So that's 100% + 10% + 10% + 220% = 340%, which is wrong. So Colton's method is wrong.
- Danielle: 75 ÷ 5 = 15 (20% of 75). Then she added 75 twice: 15 + 75 + 75 = 165 ✔️

Wait, but the question is which student got the answer wrong. So Colton's method is incorrect because his percentage breakdown is wrong (100% + 10% + 10% is 120%, not 220%). So Colton is the one who got it wrong.

Answer:

Colton