Question

A parent 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?

Answer 1

65 problems were solved correctly, 35 incorrecly.

Explanation:

1. Data:

Total answers= 100

50 cent = $0.50 for each correct answer

-30 cent = -$0.30 for each incorrect answer

Net reward= $22.00

2. Define Variables:

x= Correct answers

y= Incorrect answers

3. Formulate the Equations

Total number of answers (Eq 1)

`x+y=100\\y=100-x`

Net reward (Eq 2)

`0.50*x-0.30*y=22.00`

4. Solve by replaccing the Eq 1 in Eq 2 as follows:

`0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00`

5. Apply distrivutive property and operate:

`0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00`

6. Separate numbers and variables on each side of the equation and solve

`0.50x+0.30x=22.00+30.00\\0.80x=52.00`

7. Solve x

`x=(52.00)/(0.8) \\x=65`

Now you know that correct answers are equal to 65

8. Find Incorrect Answers with Eq 1.

`y=100-x\\y=100-65\\y=35`

Now you know that incorrect answers are equal to 35

9. Answer

65 problems were solved correctly, 35 incorrecly.

Answer 2

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