Question

Please explain how to solve the linear equation to get 20 simply, please. Thank you!

Answer 1

Raj and Aditi like to play chess against each other have won 12 of the 20 games so far. They decide to play more games.

How many more games will Aditi have to win to have a 70% winning record?

= 12 + x = 0.70 (20 + x)

= x = 20/3 = 6.67 or 7 games more

How many more games will Aditi have to win to have a 80% winning record?

Use the distributive property to multiply 0.8 by x+20.

12 + x = 0.80 (x + 20)

12 + x= 0.8x + 16

Subtract 0.8x from both sides.

12 + x − 0.8x = 16

Combine x and −0.8x to get 0.2x.

12 + 0.2x = 16

Subtract 12 from both sides.

0.2x = 16 − 12

Subtract 12 from 16 to get 4.

0.2x = 4

Divide both sides by 0.2.

x= 4/0.2

Expand 4/0.2 = 20 by multiplying both numerator and the denominator by 10.

x= 40 ÷ 2

​Divide 40 by 2 to get 20.

x=20

Answer 2

Let's solve that second equation for x

12+x = 0.80(x+20)

12+x = 0.80*x + 0.80*20

12+x = 0.80x + 16

x-0.80x = 16-12

0.2x = 4

x = 4/0.2

x = 20

So that's where the 20 comes from. It's a coincidence its the same exact value as the number of total games played so far (before the x additional games are played).