SOLUTION: Professor Johnson gives only midterm exam and a final exam. The semester average is computed by taking 1/3 of the midterm exam score plus 2/3 of the final exam score. To get a C,

Question 1092566: Professor Johnson gives only midterm exam and a final exam. The semester average is
computed by taking 1/3 of the midterm exam score plus 2/3 of the final exam score. To get a C, Beth must have a
semester average between 70 and 79 inclusive. If Beth scored only 64 on the midterm, then for what range of scores
on the final exam would Beth earn a C?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let M represent the mideterm score.
let F represent the final score.
let A represent the overall score.

the formula is A = 1/3 * M + 2/3 * F

when M = 64, this formula becomes A = 1/3 * 64 + 2/3 * F

simplify to get A = 64/3 + 2/3 * F

when A = 70, this formula becomes 70 = 1/3 * 64 + 2/3 * F

multiply both sides of this equation by 3 to get 210 = 64 + 2 * F

solve for F to get F = (210 - 64) / 2 = 73

she needs to get a 73 on the final in order for the overall score to be equal to 70.

1/3 * 64 + 2/3 * 73 = 70

when A = 79, this formula becomes 79 = 1/3 * 64 + 2/3 * F

multiply both sides of the equation by 3 to get 237 = 64 + 2 * F

solve for F to get F = (237 - 64) / 2 = 86.5

she needs to get an 86.5 on the final in order for the overall score to be equal to 79.

1/3 * 64 + 2/3 * 86.5 = 79

in order to get a C, which is any score from 70 to 79, she needs to get any score from 73 to 86.5 on the final.

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