Question

The sum of the fractions (5c-1)/(2) and (3c-4)/(4) is 18. Find the value of c.

Answer 1

To solve the given equation, we find a common denominator, combine the fractions, multiply to get rid of the denominator, and then solve for c, which results in c being equal to 6.

Step-by-step explanation:

To find the value of c given the equation (5c-1)/2 + (3c-4)/4 = 18, we need to combine these fractions into a single fraction with a common denominator:

1. First, identify a common denominator, which in this case is 4.
2. Then, rewrite each fraction with the common denominator: (2*(5c-1))/4 + (3c-4)/4.
3. Combine the numerators: ((2*(5c-1)) + (3c-4))/4.
4. The new equation is ((10c-2) + (3c-4))/4 = 18.
5. Multiply both sides by 4 to get rid of the denominator: 10c - 2 + 3c - 4 = 72.
6. Simplify and solve for c: 13c - 6 = 72, 13c = 78, c = 6.

Therefore, the value of c is 6.