Aparent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. if the child nets $22.00 after 100 problems. how many problems were solved correctly?

x = correct answer

y = incorrect answer

0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80

x= 65

y=100-65 = 35

0.5x65 = 32.50

35*0.30=10.5

32.5-10.5 = 22

 there were 65 correct answers

step-by-step :

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b