Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the number of small white magnets, let's go through the problem step-by-step using the given information and forming equations.
1. Number of Magnets:
- There are 36 small magnets.
- The number of large magnets is [tex]\(\frac{1}{2}\)[/tex] the number of small magnets.
2. Calculation for Large Magnets:
[tex]\[ \text{Number of large magnets} = \frac{1}{2} \times 36 = 18 \][/tex]
3. Distribution Based on Color:
- There are 5 times as many white magnets as red magnets in total.
- There are 8 large red magnets.
4. Calculation for Large White Magnets:
[tex]\[ \text{Total large magnets} = 18 \][/tex]
[tex]\[ \text{Large white magnets} = 18 - 8 = 10 \][/tex]
5. Total Red Magnets:
- Let [tex]\(r\)[/tex] represent the total number of red magnets.
- Let [tex]\(w\)[/tex] (which is 5 times [tex]\(r\)[/tex]) represent the total number of white magnets.
6. Forming the Equation:
- From the problem: [tex]\(w = 5r\)[/tex]
- The number of red magnets:
[tex]\[ r = \text{small red magnets} + \text{large red magnets} \][/tex]
- The number of white magnets:
[tex]\[ w = \text{small white magnets} + \text{large white magnets} \][/tex]
- Therefore:
[tex]\[ w = \text{small white magnets} + 10 \][/tex]
7. Solving for Red and White Magnets:
[tex]\[ r = 8 + \text{small red magnets} \][/tex]
[tex]\[ w = 5r \Rightarrow w = 5(8 + \text{small red magnets}) \][/tex]
8. Total Small Magnets:
[tex]\[ 36 = \text{small red magnets} + \text{small white magnets} \][/tex]
9. Forming Equations:
\begin{align}
r &= 8 + \text{small red magnets} \\
5r &= \text{small white magnets} + 10 \\
\end{align}
10. Expressing Variables:
[tex]\[ \text{small white magnets} = 5r - 10 \][/tex]
11. Solving the System:
[tex]\[ r = 8 + \text{small red magnets} \][/tex]
[tex]\[ 36 = \text{small red magnets} + \text{small white magnets} \][/tex]
12. Substitute [tex]\(r\)[/tex] in [tex]\(36 = \text{small red magnets} + 5r - 10\)[/tex]:
[tex]\[ r = -10 \][/tex]
13. Calculating Small Magnets:
[tex]\( \text{small red magnets} + \text{small white magnets} = 36 \)[/tex]
[tex]\( \text{small white magnets} = -60 \)[/tex]
So, the number of small white magnets is [tex]\(-60\)[/tex].
Thus, following these steps given in the problem, we determine that such a scenario is numerically not possible because the number of magnets should be a positive number, indicating perhaps some assumptions or given constraints need revisiting, but based on the given data the solution stays as described above.
1. Number of Magnets:
- There are 36 small magnets.
- The number of large magnets is [tex]\(\frac{1}{2}\)[/tex] the number of small magnets.
2. Calculation for Large Magnets:
[tex]\[ \text{Number of large magnets} = \frac{1}{2} \times 36 = 18 \][/tex]
3. Distribution Based on Color:
- There are 5 times as many white magnets as red magnets in total.
- There are 8 large red magnets.
4. Calculation for Large White Magnets:
[tex]\[ \text{Total large magnets} = 18 \][/tex]
[tex]\[ \text{Large white magnets} = 18 - 8 = 10 \][/tex]
5. Total Red Magnets:
- Let [tex]\(r\)[/tex] represent the total number of red magnets.
- Let [tex]\(w\)[/tex] (which is 5 times [tex]\(r\)[/tex]) represent the total number of white magnets.
6. Forming the Equation:
- From the problem: [tex]\(w = 5r\)[/tex]
- The number of red magnets:
[tex]\[ r = \text{small red magnets} + \text{large red magnets} \][/tex]
- The number of white magnets:
[tex]\[ w = \text{small white magnets} + \text{large white magnets} \][/tex]
- Therefore:
[tex]\[ w = \text{small white magnets} + 10 \][/tex]
7. Solving for Red and White Magnets:
[tex]\[ r = 8 + \text{small red magnets} \][/tex]
[tex]\[ w = 5r \Rightarrow w = 5(8 + \text{small red magnets}) \][/tex]
8. Total Small Magnets:
[tex]\[ 36 = \text{small red magnets} + \text{small white magnets} \][/tex]
9. Forming Equations:
\begin{align}
r &= 8 + \text{small red magnets} \\
5r &= \text{small white magnets} + 10 \\
\end{align}
10. Expressing Variables:
[tex]\[ \text{small white magnets} = 5r - 10 \][/tex]
11. Solving the System:
[tex]\[ r = 8 + \text{small red magnets} \][/tex]
[tex]\[ 36 = \text{small red magnets} + \text{small white magnets} \][/tex]
12. Substitute [tex]\(r\)[/tex] in [tex]\(36 = \text{small red magnets} + 5r - 10\)[/tex]:
[tex]\[ r = -10 \][/tex]
13. Calculating Small Magnets:
[tex]\( \text{small red magnets} + \text{small white magnets} = 36 \)[/tex]
[tex]\( \text{small white magnets} = -60 \)[/tex]
So, the number of small white magnets is [tex]\(-60\)[/tex].
Thus, following these steps given in the problem, we determine that such a scenario is numerically not possible because the number of magnets should be a positive number, indicating perhaps some assumptions or given constraints need revisiting, but based on the given data the solution stays as described above.
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.