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

she has 16 correct answer

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*\left( 2\right)\end{cases}`

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

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