Question

Raj and Aditi like to play chess against each other. Aditi has 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 = ≈ 6.67 She will have to win 7 more games to have a 70% winning record. How many more games will Aditi have to win to have an 80% winning record? The linear equation that models this is . Aditi would have to win more games to have an 80% winning record.

Answer 1

20

Explanation:

We are given that she have to win games to have a 70% winning record :

`12 + x = 0.70(20 + x)`

`x = 6.67`

So, She will have to win 7 more games to have a 70% winning record.

Now we are supposed to find how many more games will she have to win to have an 80% winning record

So, equation becomes:

`12 + x = 0.80(20 + x)`

`12 + x = 16 + 0.8x`

`x-0.8x= 16 -12`

`0.2x= 4`

`x= (4)/(0.2)`

`x=20`

Answer 2

12 + x = 0.80(20+x)
12 + x = 16 + 0.80x
12 = 16 -0.2x
-4 = -0.2x

x = -4/-0.2 = 20
they need to win 20 more games