Question

Given the equations:

A. 2x+10=kc
B. 4x+1=cn

If the sum of cn equals 31, what are the values of k and c?

Answer 1

After solving the system of equations step by step, starting by finding x using the equation 4x + 1 = cn, we determine that the values of k and c are k = 25 and c = 1.

Step-by-step explanation:

To find the values of k and c given the equations:

• A. 2x+10 = kc
• B. 4x+1 = cn

And knowing that the sum of cn equals 31, we can solve for c and k as follows:

1. From equation B, since cn = 31, we can write it as 4x + 1 = 31.
2. To find x, we subtract 1 from both sides: 4x = 31 - 1.
3. Dividing both sides by 4 gives us x = 30/4 = 7.5.
4. Now that we have x, substitute x = 7.5 into equation A (2x + 10 = kc) to find k and c.
5. 2(7.5) + 10 = kc simplifies to 15 + 10 = kc, which simplifies further to 25 = kc.
6. We can use the value of cn (which is 31) and the value of x to find c: 4(7.5) + 1 = 31, so 30 + 1 = 31.
7. Now knowing that c multiplied by a number gives us 31, we can deduce that c = 1.
8. Finally, we can use the derived c value to find k: since 25 = k(1), k = 25.

The values are therefore k = 25 and c = 1.