On a standardized test the final scores are calculated by averaging the math, science, and literature scores. Kelly's math score is 84%, and her literature score is 1.25 times her science score. Find her science and literature scores if her final score is 82%.

Kelly's science score is 72%.

Kelly's literature score is 90%.

Step-by-step explanation:

It is given that,

Her literature score is 1.25 times her science score.

Let us assume that, her science score is x.

Kelly's science score is x Kelly's literature score is 1.25x Kelly's math score is 84%.

On a standardized test,

The final scores are calculated by averaging the math, science, and literature scores.

We know that, her final score is 82%. Average = (Math + science + Literature) / 3

To find the science score:

⇒ 82 = (84 + x + 1.25x) / 3

⇒ 82 * 3 = (84 + 2.25x)

⇒ 246 = 84 + 2.25x

⇒ 246 - 84 = 2.25x

⇒ 162 = 2.25x

⇒ x = 162 / 2.25

⇒ x = 72

∴ Kelly's science score is 72%.

To find the literature score:

Kelly's literature score is 1.25x

Substitute x = 72,

⇒ 1.25 * 72

⇒ 90

∴ Kelly's literature score is 90%.