Answer:
k = 35, c = 65
Explanation:
Solve the following system:
{c + k = 100 | (equation 1)
{11 c + 51 k = 2500 | (equation 2)
Swap equation 1 with equation 2:
{11 c + 51 k = 2500 | (equation 1)
{c + k = 100 | (equation 2)
Subtract 1/11 × (equation 1) from equation 2:
{11 c + 51 k = 2500 | (equation 1)
{0 c - (40 k)/11 = -1400/11 | (equation 2)
Multiply equation 2 by -11/40:
{11 c + 51 k = 2500 | (equation 1)
{0 c+k = 35 | (equation 2)
Subtract 51 × (equation 2) from equation 1:
{11 c+0 k = 715 | (equation 1)
{0 c+k = 35 | (equation 2)
Divide equation 1 by 11:
{c+0 k = 65 | (equation 1)
{0 c+k = 35 | (equation 2)
Collect results:
Answer: {c = 65 , k = 35