Question

Explain reasoning!

1.) If you make 20% more money than me, then I make 20% less than you.

2.)If I have an average of 60% before the final , then I must score 80% on the final in order to raise my average up to 70% to pass the this Math 75 class.

Answer 1

1.) Incorrect,

2.) Correct

Explanation:

1.) Let x be the amount of money,

After increasing x by 20%,

New amount of money ( say y )= (100+20)% of x ( i.e. y is 20% more than x )

= 120 % of x

`=(120x)/(100)`

⇒ y = 1.20x

`\because (y-x)/(y)* 100=( 1.20x-x)/(1.20x)* 100`

`=(0.2x)/(1.2x)* 100`

`=(20)/(1.2)`

≈ 16.67%

Thus, x is approximately 16.67% less than y.

2.) First score = 60%,

Second score = x% ( let )

So, Average percentage score =
`(60+x)/(2)`

If
`(60+x)/(2)=70`

`60+x=140\implies x = 80`