Q45. - 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.

Write a system of equations that represents the number of each type of question

Step-by-Step Solution

Answer

The equations so formed for the given question is 

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

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

Let us suppose the number of true/false questions be x and the number of multiple-choice questions be y.

Now according to the question, the true/false questions are worth 2 points each and multiple-choice questions are 4 points each which together constitutes $100$ points.

The first equation so formed is below.

$2x+4y=100$

Step-3 – Formation of the equations

Consider the second statement.

There are twice multiple-choice questions as true/false, which can be mathematically expressed as.

$y=2x$

Hence, both the equations so formed for the given question are 

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