There are 20 students in a math class who have brown hair. This represents 80 percent of the students in the class. Which equati
on can be used to find the total number of students in the math class?
2 answers:
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<u>ANSWER</u>
The equation has no solution if
and
.
<u>EXPLANATION</u>
The first equation is
and the second equation is
We try solving this equation for B using the <em>method of elimination.</em>
We multiply equation (2) by 3 to obtain;
We also multiply equation (1) by B to obtain;
We now subtract equation (3) from equation (4).
This will give us;
We factor on the right hand side to get;
We solve for y to obtain;
The above equation is defined for all real values except
This implies that
Remember that the system will have no solution if and only if the denominator is zero and the numerator is not equal to zero.
This means that,
When we substitute , then we will have
Hence the correct answer is option A
<em>Note however that if both the numerator and denominator equal zero, then the system has infinitely many solutions.</em>