I need help with the math riddle

[mikeyp]

To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every right question she answered and fined her $5 for every incorrect solution. At the end of the first 26 problems, neither of them owed any money to each other. How many problems did the daughter solve correctly?

I'm thinking 10. As 10x8=80 and -5x16=80

 

[soroban]

Hello, mikeyp!

To stimulate his daughter in the pursuit of problem solving,
a math professor offered to pay her $8 for correct solution
and fined her $5 for every incorrect solution.

At the end of the first 26 problems, neither of them owed any money to each other.
How many problems did the daughter solve correctly?

I'm thinking 10 . . . As 10 x 8 = 80 and -5 x 16 = 80

Did you get your answer by trial-and-error or did you use Algebra?

Let R = number of right answers.
Then 26 - x = number of wrong answers.

She gave R right answers and won $8 each.
. . She won 8R dollars.

She gave 26 - R wrong answers and lost $5 each.
. . She lost 5(26 - R) dollars.

Since they "broke even", her winnings equal her losss.

We have: .8R .= .5(26 - R)

. . . . . . . . 8R .= .130 - 5R

. . . . . . . 13R .= .130

. . . . . . . . . R .= .10


Therefore, she had 10 correct answers.