Question 136710
Let C = the number of correct solutions and I = the number of incorrect soltion.
1) {{{C+I = 26}}} The total number of problems is 26.
2) {{{C(8) - I(5) = 0}}} $8 times the number of correct solutions minus $5 times the number of incorrect solutions is zero.
Rewrite equation 1) as:
{{{I = 26-C}}} and substitute into equation 2):
{{{C(8)-(26-C)5 = 0}}} Simplify and solve for C.
{{{8C-(130-5C) = 0}}}
{{{13C-130 = 0}}} Add 130 to both sides.
{{{13C = 130}}} Divide both sides by 13.
{{{C = 10}}} The number of correctly solved problems is 10.
Check:
{{{10(8)-16(5) = 80-80}}}={{{0}}}