If A/3=b/4=c/7 , find The Value Of A + B + C /c (a) 7 (b) 2 (c) 1/2 (d) 1/7
110. If a/3=b/4=c/7, find the value of a + b + c / c
In this problem, we are given a set of equations involving the variables a, b, and c. We need to find the value of the expression a + b + c divided by c. To solve this problem, we will first manipulate the given equations to find the values of a, b, and c. Then, we will substitute these values into the expression a + b + c / c to find the final answer.
Step 1: Manipulate the Given Equations
We are given the equations a/3 = b/4 = c/7. To eliminate the fractions, we can multiply both sides of each equation by the least common multiple (LCM) of the denominators. The LCM of 3, 4, and 7 is 84.
a/3 = b/4 = c/7
84(a/3) = 84(b/4) = 84(c/7)
28a = 21b = 12c
Step 2: Find the Values of a, b, and c
We can now use the equations 28a = 21b = 12c to find the values of a, b, and c. We can start by setting 28a = 21b and solving for a in terms of b.
28a = 21b
a = (21/28)b
a = (3/4)b
Similarly, we can set 28a = 12c and solve for a in terms of c.
28a = 12c
a = (12/28)c
a = (3/7)c
We can now equate the two expressions for a and solve for b in terms of c.
(3/4)b = (3/7)c
b = (7/4)c
Step 3: Find the Value of a + b + c / c
Now that we have found the values of a, b, and c in terms of c, we can substitute these values into the expression a + b + c / c.
a + b + c / c = ((3/7)c) + ((7/4)c) + c / c
= (3/7)c + (7/4)c + c / c
= ((12/28)c + (21/28)c + (28/28)c) / c
= (61/28)c / c
= 61/28
In this problem, we were given a set of equations involving the variables a, b, and c. We manipulated the equations to find the values of a, b, and c in terms of c. Then, we substituted these values into the expression a + b + c / c to find the final answer. The value of a + b + c / c is 61/28.
The final answer is 61/28.
110. If a/3=b/4=c/7, find the value of a + b + c / c: Q&A
In our previous article, we solved the problem of finding the value of a + b + c / c given the equations a/3 = b/4 = c/7. In this article, we will provide a Q&A section to help clarify any doubts and provide additional insights into the problem.
Q: What is the least common multiple (LCM) of 3, 4, and 7?
A: The LCM of 3, 4, and 7 is 84.
Q: Why did we multiply both sides of each equation by the LCM?
A: We multiplied both sides of each equation by the LCM to eliminate the fractions. This made it easier to work with the equations and find the values of a, b, and c.
Q: How did we find the values of a, b, and c in terms of c?
A: We found the values of a, b, and c in terms of c by setting 28a = 21b and solving for a in terms of b, and then setting 28a = 12c and solving for a in terms of c. We also equated the two expressions for a and solved for b in terms of c.
Q: Why did we substitute the values of a, b, and c into the expression a + b + c / c?
A: We substituted the values of a, b, and c into the expression a + b + c / c to find the final answer. This allowed us to simplify the expression and find the value of a + b + c / c.
Q: What is the final answer to the problem?
A: The final answer to the problem is 61/28.
Q: What if the equations were a/3 = b/5 = c/7? How would we solve the problem?
A: If the equations were a/3 = b/5 = c/7, we would follow the same steps as before. We would multiply both sides of each equation by the LCM (which is 105), and then find the values of a, b, and c in terms of c. We would then substitute these values into the expression a + b + c / c to find the final answer.
Q: Can we use this method to solve other problems involving equations with fractions?
A: Yes, we can use this method to solve other problems involving equations with fractions. The key is to multiply both sides of each equation by the LCM to eliminate the fractions, and then find the values of the variables in terms of one of the variables.
Q: What if the equations were a/3 = b/4 = c/7, but the expression was a + b + c / a instead of a + b + c / c? How would we solve the problem?
A: If the expression was a + b + c / a instead of a + b + c / c, we would follow the same steps as before. We would multiply both sides of each equation by the LCM (which is 84), and then find the values of a, b, and c in terms of c. We would then substitute these values into the expression a + b + c / a to find the final answer.
In this Q&A article, we provided additional insights and clarification on the problem of finding the value of a + b + c / c given the equations a/3 = b/4 = c/7. We also answered some frequently asked questions and provided examples of how to apply the method to other problems involving equations with fractions.