lisa is currently taking physics as one of her electives in school. her grade at the end of the year is…

lisa is currently taking physics as one of her electives in school. her grade at the end of the year is determined by the average of four exams, each worth 100 points. on her first test she got an 84, on her second she got a 92, and on her third an 80. what must she score on her fourth exam to get exactly 80% in the course?\na. 60\nb. 64\nc. 84\nd. 85

lisa is currently taking physics as one of her electives in school. her grade at the end of the year is determined by the average of four exams, each worth 100 points. on her first test she got an 84, on her second she got a 92, and on her third an 80. what must she score on her fourth exam to get exactly 80% in the course?\na. 60\nb. 64\nc. 84\nd. 85

Answer

Explanation:

Step1: Set up the average - formula

The average of four numbers (x_1,x_2,x_3,x_4) is (\bar{x}=\frac{x_1 + x_2+x_3+x_4}{4}). We know that (\bar{x} = 80), (x_1=84), (x_2 = 92), (x_3=80), and we want to find (x_4).

Step2: Substitute the known values into the formula

(80=\frac{84 + 92+80+x_4}{4}).

Step3: Multiply both sides by 4

(80\times4=84 + 92+80+x_4). (320=84 + 92+80+x_4).

Step4: Calculate the sum of the known numbers

(84+92 + 80=256).

Step5: Solve for (x_4)

(320=256+x_4). (x_4=320 - 256). (x_4 = 64).

Answer:

b. 64