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The number of fruits purchased by Ms. Paul is given by the following two equations, where a, b and c are the number of apples, bananas and oranges, respectively:
3a - 4b + 2c = 0
4a - 2b - c = 0
4a - 2b - c = 0
Which of the following represents the ratio of the numbers of apples, bananas and oranges purchased by Ms. Paul?
- a)16 : 22 : 20
- b)8 : 10 : 22
- c)16 : 10 : 22
- d)10 : 20 : 22
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The number of fruits purchased by Ms. Paul is given by the following t...
3a - 4b + 2c = 0 ... (1)
4a - 2b - c = 0 ... (2)
From equation (2),
c = 4a - 2b
Substituting the value of c = 4a - 2b in (1), we get
3a - 4b + 8a - 4b = 0
Or 11a = 8b
Further, c = 4a - 2b
Multiplying by 4 on both sides, we get
4c = 16a - 8b
Substituting 8b = 11a, we get
4c = 16a - 11a = 5a
Or a : b : c = a : 11a/8 : 5a/4
So, option 1 is the answer.
4a - 2b - c = 0 ... (2)
From equation (2),
c = 4a - 2b
Substituting the value of c = 4a - 2b in (1), we get
3a - 4b + 8a - 4b = 0
Or 11a = 8b
Further, c = 4a - 2b
Multiplying by 4 on both sides, we get
4c = 16a - 8b
Substituting 8b = 11a, we get
4c = 16a - 11a = 5a
Or a : b : c = a : 11a/8 : 5a/4
= 8 : 11 : 1
0 or 16 : 22 : 2
0So, option 1 is the answer.
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Community Answer
The number of fruits purchased by Ms. Paul is given by the following t...
To solve this problem, we need to find the values of a, b, and c that satisfy the given equations.
First, let's rewrite the equations in a more standard form:
3a - 4b + 2c = 0 ...(1)
4a - 2b - c = 0 ...(2)
To solve these equations, we can use the method of elimination or substitution. Let's use the method of elimination:
1. Multiply equation (2) by 2:
8a - 4b - 2c = 0 ...(3)
2. Add equation (1) and equation (3):
(3a - 4b + 2c) + (8a - 4b - 2c) = 0
Simplifying, we get:
11a - 8b = 0
3. Solve equation (4) for a:
11a = 8b
a = (8b)/11
4. Substitute the value of a in equation (1):
3((8b)/11) - 4b + 2c = 0
Simplifying, we get:
(24b - 44b)/11 + 2c = 0
-20b/11 + 2c = 0
2c = (20b)/11
c = (10b)/11
5. Substitute the values of a and c in equation (2):
4((8b)/11) - 2b - ((10b)/11) = 0
Simplifying, we get:
(32b - 22b - 10b)/11 = 0
0 = 0
Since the equation 0 = 0 is always true, it means that the values of a, b, and c can take any value and still satisfy the given equations.
So, there are infinitely many possible solutions to these equations, and we cannot determine the exact ratio of the numbers of apples, bananas, and oranges purchased by Ms. Paul.
Therefore, none of the given options (a), (b), (c), or (d) represents the correct ratio.
First, let's rewrite the equations in a more standard form:
3a - 4b + 2c = 0 ...(1)
4a - 2b - c = 0 ...(2)
To solve these equations, we can use the method of elimination or substitution. Let's use the method of elimination:
1. Multiply equation (2) by 2:
8a - 4b - 2c = 0 ...(3)
2. Add equation (1) and equation (3):
(3a - 4b + 2c) + (8a - 4b - 2c) = 0
Simplifying, we get:
11a - 8b = 0
3. Solve equation (4) for a:
11a = 8b
a = (8b)/11
4. Substitute the value of a in equation (1):
3((8b)/11) - 4b + 2c = 0
Simplifying, we get:
(24b - 44b)/11 + 2c = 0
-20b/11 + 2c = 0
2c = (20b)/11
c = (10b)/11
5. Substitute the values of a and c in equation (2):
4((8b)/11) - 2b - ((10b)/11) = 0
Simplifying, we get:
(32b - 22b - 10b)/11 = 0
0 = 0
Since the equation 0 = 0 is always true, it means that the values of a, b, and c can take any value and still satisfy the given equations.
So, there are infinitely many possible solutions to these equations, and we cannot determine the exact ratio of the numbers of apples, bananas, and oranges purchased by Ms. Paul.
Therefore, none of the given options (a), (b), (c), or (d) represents the correct ratio.
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The number of fruits purchased by Ms. Paul is given by the following two equations, wherea,bandcare the number of apples, bananas and oranges, respectively:3a- 4b+ 2c= 04a- 2b-c= 0Which of the following represents the ratio of the numbers of apples, bananas and oranges purchased by Ms. Paul?a)16 : 22 : 20b)8 : 10 : 22c)16 : 10 : 22d)10 : 20 : 22Correct answer is option 'A'. Can you explain this answer?
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