Create and solve a one-variable linear equation from a short context.
Write an equation for an average or mixture
Problem
A student has test scores of \(80\) and \(90\). Write an equation for the third score \(x\) needed to produce an average of \(85\), and solve for \(x\).
Big Picture
What this problem is really about
An average links two totals: the sum of all scores and the number of scores. We’ll include the unknown score in the complete sum, divide that grouped sum by the full count, and set the result equal to the target average. Clearing the denominator gives the required total, so the missing score can then be isolated.
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