Home > AC > Chapter 9 > Lesson 9.2.1 > Problem9-30

9-30.

Solve the problem below by writing and solving one or two equations. A Guess and Check table may help you get started. Be sure to define your variable(s) and write your solution as a sentence.

Rowan received $3$ points for each question he answered correctly on Part 1 of a test and 2 points for each question he answered correctly on Part 2. If he answered $33$ questions correctly and received a total of $85$ points, how many questions did he answer correctly on Part 1?

$x =$ # of correct answers on Part 1
$y=$ # of correct answers on Part 2

Write a set of equations representing the problem.

$\begin{array}{l} x + y = 33 \\ 3x + 2y = 85 \end{array}$

Solve the second equation for $y$.

$y=33-x$

Substitute $33-x$ in for $y$.

$3x+2\left(33-x\right)=85$

Solve for $x$.

$3x+66-2x=85$

$x=19$

Substitute $19$ into one of the original equations for $x$.

$19+y=33$

Solve for $y$.

$y=14$