Q47. - Algebra 2

Question

Mr. Talbot is writing a test for his science classes. The test will have true/false questions worth 2 points each and multiple-choice questions worth 4 points each for a total of $100$ points. He wants to have twice as many multiple-choice questions as true/false.

$47.$ If most of his students can answer true/false questions within 1 minute and multiple-choice questions within $1\frac{1}{2}$ minutes, will they have enough time to finish the test in $45$ minutes?

Step-by-Step Solution

Answer

Yes, $45$ minutes will be enough to finish the test.

Step-1 – Apply the concept of system of equations

A set of two or more equations with the same variables is called a system of linear equations. The ordered pairs that satisfy all the equations in the system is called as solution of the equations.

Step-2 – Formation of the equations

Here, x represents the number of true/false questions and y represents the number of multiple-choice questions. The equations so formed according to the question are:

$\begin{array}{c}2x+4y=100\\ y=2x\end{array}$

Step-3 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-4 – Description of step

Since, most of the students can answer true/false questions in 1 minute and multiple-choice questions in $1\frac{1}{2}$ minutes.

Now there are $10$ true/false questions and $20$ multiple-choice questions. So, total time taken to solve these $30$ questions will be.

$\begin{array}{c}10\left(1\right)+20\left(\frac{3}{2}\right)=10+\left(10*3\right)\\ =10+30\\ =40\end{array}$

Thus, the time taken to solve these questions is $40$ minutes.

Hence, $45$ minutes will be enough to finish the test.