Anna sold her muffins to earn allowance during school vacation. The number of $2, $5 and $10-notes she earned were in ratio of 5 : 3 : 2. The notes were worth $1125 altogether. How many $2-notes were there?
Question
Anna sold her muffins to earn allowance during school vacation. The number of 5 and 1125 altogether. How many $2-notes were there?
Solution 1
To solve this problem, we need to follow these steps:
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First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
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Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
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Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
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Finally, we need to find out how many 2 notes is 5, we multiply the value of each part of the ratio by 5. So, 562.5. But since we can't have half a note, we need to understand that each 562.5 by 2 to get the actual number of 562.5 ÷ 2 = 281.25. Again, we can't have a quarter of a note, so we round this number to the nearest whole number. Therefore, Anna had approximately 281 $2 notes.
Solution 2
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio. The ratio of the number of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
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Finally, we need to find the number of 2 notes is 5. So, we multiply the value of each ratio by the ratio of 112.5 x 5 = 2. Therefore, 2 = 281.25. But since we can't have a quarter of a note, it means that the number of $2 notes is 281.
Solution 3
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find out how many 2 notes is 5, we multiply the value of each part of the ratio by 5. So, 562.5. But since we can't have half a note, it means that each part of the ratio is actually worth double, or 2 notes is $562.5 ÷ 2 = 281.25, which rounds down to 281.
So, there were 281 $2 notes.
Solution 4
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find out how many 2 notes is 5, we multiply the value of each part of the ratio by 5. So, 562.5. But since we can't have half a note, it means that we've made a mistake in our calculations.
The mistake lies in step 3. We assumed that each part of the ratio corresponds to the same amount of money. But in reality, each part of the ratio corresponds to a different amount of money, depending on the value of the note.
So, let's correct this. Let's say that the number of 5 notes is 3x, and the number of 25x + 102x = $1125.
Solving this equation gives x = 45.
So, the number of $2 notes is 5x = 5*45 = 225.
So, there were 225 $2 notes.
Solution 5
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio. The ratio of the number of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total number of parts in the ratio. We do this by adding the numbers in the ratio together. So, 5 + 3 + 2 = 10 parts.
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We know that the total value of all the notes is 1125 ÷ 10 = 112.5.
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We want to find out how many 2 notes make up 5 parts. So, we multiply the value of one part by 5. So, 562.5. This is the total value of the $2 notes.
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Finally, to find the number of 2 notes by the value of each note. So, $562.5 ÷ 2 = 281.25.
However, the number of notes should be a whole number, and it's not possible to have 0.25 of a note. This suggests that there may be a mistake in the problem as it's currently stated.
Solution 6
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio. The ratio of the number of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find the number of 2 notes is 5. So, we multiply the value of each ratio by the ratio of 112.5 x 5 = $562.5. But since we can't have half a note, it means we made a mistake in our calculations.
The mistake is that we didn't consider the value of each note in the ratio. The correct way to solve the problem is:
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The total ratio represents the total number of notes, not their value. So, we have 5 parts of 5 notes, and 2 parts of 45 for each complete set of notes in the ratio.
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Now, we divide the total value of the notes by the value of each complete set to find out how many complete sets we have. So, 45 = 25 sets.
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Finally, we find the number of 2 notes. So, 25 sets * 5 (the ratio for 2 notes.
So, Anna had 125 $2 notes.
Solution 7
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find out how many 2 notes is 5, we multiply the value of each part of the ratio by 5. So, 562.5. But since we can't have half a note, it means that each part of the ratio is actually worth double, or 2 notes is $562.5 ÷ 2 = 281.25, which is not possible.
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Therefore, we need to reconsider the value of each part of the ratio. If each part is worth 2 notes is $225 x 5 ÷ 2 = 562.5, which is still not possible.
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The problem seems to be in the interpretation of the problem. The ratio given is not of the number of notes, but of the total value of each type of note. So, the 5 notes are worth 3 parts, and the $10 notes are worth 2 parts.
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If we reconsider the problem this way, then each part is worth 112.5.
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Therefore, the total value of the 112.5/part = $562.5.
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Since each 2, the number of 562.5 ÷ $2/note = 281.25 notes, which is still not possible.
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Therefore, there seems to be a mistake in the problem. The total value of the notes and the given ratio do not allow for a whole number of $2 notes.
Solution 8
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find out how many 2 notes is 5, we multiply the value of each ratio by 5. So, 562.5. But since we can't have half a note, there must be some mistake.
The mistake lies in the fact that we didn't consider the value of the notes in the ratio. The correct approach would be:
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Assign the ratios to the respective note values: 5 notes = 3x, $10 notes = 2x.
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Set up the equation according to the total value of the notes: 2*(5x) + 5*(3x) + 10*(2x) = $1125.
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Solve the equation to find the value of x: 10x + 15x + 20x = 1125, 45x = 1125, x = 1125 ÷ 45, x = 25.
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Substitute x = 25 into 5x to find the number of $2 notes: 5*25 = 125.
So, there were 125 $2 notes.
Solution 9
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio of the notes. The ratio of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total ratio. We do this by adding the individual ratios together. So, 5 + 3 + 2 = 10.
-
Now, we know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
Finally, we need to find out how many 2 notes is 5, we multiply the value of each part of the ratio by 5. So, 562.5. But since we can't have half a note, it means that each part of the ratio is actually worth double, or 2 notes is $562.5 ÷ 2 = 281.25, or 281 when rounded down to the nearest whole number.
So, Anna had 281 $2 notes.
Solution 10
To solve this problem, we need to follow these steps:
-
First, we need to understand the ratio. The ratio of the number of 5, and 2 notes, there are 3 10 notes.
-
Next, we need to find the total number of parts in the ratio. We do this by adding the numbers in the ratio together. So, 5 + 3 + 2 = 10 parts.
-
We know that the total value of all the notes is 1125 ÷ 10 = 112.5.
-
We want to find out how many 2 notes are represented by 5 parts in the ratio. So, we multiply the value of each part by the number of parts for the 112.5 x 5 = 2 notes.
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Finally, to find the number of 2 notes by the value of each note. So, $562.5 ÷ 2 = 281.25.
However, the number of notes should be a whole number, and it's not possible to have 0.25 of a note. This suggests that there might be a mistake in the problem as it's currently stated.
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