Calculate Remaining Horses: 47 Total - (3 × 10) Paddock Capacity Problem

Subtraction Problems with Capacity Constraints

There are 47 horses in total in a field. Next to the field there are three paddocks, each with a capacity for 10 horses.

How many horses will remain in the field once each of the paddocks is filled?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

There are 47 horses in total in a field. Next to the field there are three paddocks, each with a capacity for 10 horses.

How many horses will remain in the field once each of the paddocks is filled?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the total capacity of the paddocks.
  • Step 2: Subtract the total paddock capacity from the total number of horses.

Let's proceed with each step:

Step 1: Calculate the total capacity of the paddocks.
Each paddock can hold 10 horses. There are 3 paddocks, so the total capacity is:

3×10=30 3 \times 10 = 30

Step 2: Subtract the total paddock capacity from the total number of horses.
We start with 47 horses. Placing 30 horses in the paddocks leaves:

4730=17 47 - 30 = 17

Therefore, the number of horses that will remain in the field is 17 17 .

3

Final Answer

17 17

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Calculate total capacity before finding remaining amount
  • Method: Multiply 3 paddocks × 10 capacity = 30 horses
  • Check: Verify 47 - 30 = 17, then 17 + 30 = 47 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting individual paddock capacities separately
    Don't subtract 47 - 10 - 10 - 10 = 17 step by step! This takes longer and increases chance of arithmetic errors. Always calculate total capacity first: 3 × 10 = 30, then subtract once: 47 - 30 = 17.

Practice Quiz

Test your knowledge with interactive questions

If we have 85 blocks in total, how many blocks will remain if we remove 4 tens and 1 one?

FAQ

Everything you need to know about this question

Why do I multiply 3 × 10 instead of just subtracting 10 three times?

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Multiplication is more efficient! When you have equal groups, multiply to find the total quickly. 3 × 10 = 30 is faster than 10 + 10 + 10 = 30 and reduces calculation errors.

What if the paddocks had different capacities?

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Then you'd add the individual capacities instead of multiplying. For example: if paddocks hold 8, 12, and 10 horses, total capacity = 8 + 12 + 10 = 30.

How can I check if my answer makes sense?

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Ask yourself: "Could 17 horses fit in the field?" Since we moved 30 horses out of 47 total, having 17 remaining is reasonable - it's less than half the original amount.

What if there were more horses than total paddock capacity?

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The same method works! If you had 60 horses and 30 paddock spaces, then 60 - 30 = 30 horses would remain in the field. There's always enough room in the field for the extras.

Do I need to worry about the order of operations here?

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Yes, but it's simple! Always do multiplication first: 3 × 10 = 30, then subtraction: 47 - 30 = 17. Following PEMDAS ensures you get the right answer.

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