<think>Okay, let's see. The problem says that Weng earns $12 an hour for babysitting, and yesterday she only did 50 minutes. We need to figure out how much she earned. Hmm, right, it's about converting minutes to hours since her rate is per hour. 

First, I should recall that 1 hour is 60 minutes. So, 50 minutes is less than an hour. I need to find out what fraction of an hour 50 minutes is. To do that, I can divide 50 by 60. Let me write that down: 50 divided by 60. That should give me the decimal equivalent of how many hours she worked. 

Calculating that, 50 ÷ 60. Let's do the division. 50 divided by 60. So, 60 goes into 50 zero times. Then add a decimal point. 60 goes into 500 eight times because 60 x 8 is 480. Subtract 480 from 500, we get 20. Bring down another 0 to make 200. 60 goes into 200 three times (60x3=180). Subtract 180 from 200, we get 20 again. This seems like it's repeating. So 50/60 is 0.833333... which is 0.833 recurring. I can write that as 0.833... or round it to maybe two decimal places, 0.83 or three decimal places 0.833 perhaps. But maybe we should keep it exact as a fraction. Oh, right! 50 minutes is 50/60 of an hour, which simplifies to 5/6. Because 50 divided by 10 is 5, and 60 divided by 10 is 6. So 5/6 of an hour.

Therefore, instead of converting to a decimal, I can work with the fraction 5/6. So her earnings would be 12 dollars multiplied by 5/6. Let me compute that. 

12 multiplied by 5 is 60. Then 60 divided by 6 is 10. So 12 * (5/6) = 10. That seems straightforward. Wait, let me check that again. 12 divided by 6 is 2, and 2 multiplied by 5 is 10. Yes, that's correct. So 10 dollars. 

Alternatively, if I had converted 50 minutes to hours as a decimal first, 0.8333... multiplied by 12. Let's try that. 12 * 0.8333... 12 times 0.8 is 9.6, and 12 times 0.0333... is approximately 0.4. Adding them up: 9.6 + 0.4 = 10. So that also gives 10 dollars. Either way, same answer. 

Wait, just to make sure: Is 5/6 of an hour indeed equal to 50 minutes? Since 1 hour is 60 minutes, each 10 minutes would be 1/6 of an hour. So 50 minutes is 5 times 10 minutes, which is 5/6 hour. Yeah, that checks out. 

So Weng earned $10 for her 50 minutes of babysitting. Let me just summarize the steps again. First, convert the time she worked from minutes to hours by dividing by 60. Either as a fraction (50/60 = 5/6) or a decimal (≈0.8333). Multiply this by her hourly rate of $12, resulting in $10. Both methods confirm the same answer. I think that's solid. 

I should also consider if there's another way to approach this, maybe by figuring out how much she makes per minute and then multiplying by 50 minutes. Let's try that as a verification. 

Since she makes $12 per hour, that's $12 for 60 minutes. So per minute, she earns 12/60 = $0.20 per minute. Then, 50 minutes would be 50 * 0.20 = $10. Exactly the same result. 

So using three different methods—fraction of an hour, decimal conversion, and per-minute rate—all give the same answer of $10. Definitely confident that's correct. 

I can't think of any mistakes here. The calculations are straightforward and cross-verified. The key is ensuring the conversion from minutes to hours is correct, which I checked multiple times. Even using different methods: fractions, decimals, and unit rate. All align. Therefore, the final answer must be $10.
</think>

Weng earns $12 per hour for babysitting and worked for 50 minutes. To calculate her earnings, follow these steps:

1. **Convert 50 minutes to hours**:  
   Since 1 hour = 60 minutes:  
   \(\frac{50}{60} = \frac{5}{6}\) hours (or ≈0.833 hours).

2. **Calculate earnings**:  
   Multiply the hourly rate by the fraction of the hour worked:  
   \(\$12 \times \frac{5}{6} = \$10\)  
   **Verification**:  
   - **Per-minute rate**: \(\$12/60 = \$0.20\) per minute.  
     Earnings: \(50 \times \$0.20 = \$10\).  
   - **Decimal conversion**: \(0.833... \times 12 ≈ \$10\).

All methods confirm the final answer.  

\(\boxed{10}\)