Question

At a math contest 20problems we’re given each correct answer earned 5 points and 2 points were deducted for each incorrect answer Lenore answer all the problem receiving a score of 72 how many correct answer did she have

Answer 1

Answer:

she has 16 correct answer

Step-by-step explanation:

Mathematically ,we can translate this word problem into this system of equations :

$\begin{cases}5x-2y=72&\left( 1\right) \\ x+y=20&\left( 2\right)\end{cases}$

$\Longleftrightarrow \begin{cases}5x-2y=72&\left( 1\right) \\ 2x+2y=40&2\times\left( 2\right)\end{cases}$

$\Longleftrightarrow \begin{cases}7x=72+40=112&\left( 1\right)+2\times(2) \\ x+y=20&\left( 2\right)\end{cases}$

$\Longleftrightarrow \begin{cases}x=\frac{112}{7}=16 \\ y=20-x=20-16=4&\left( 2\right)\end{cases}$