# Video: US-SAT03S3-Q14-536185030627

The formula πΈ = (π + 3π + πΏ)/7 is often used by teachers to compute the estimated time needed by students to complete homework, πΈ, where π the shortest completion time, πΏ the longest, and π the most likely. Which of the following correctly gives πΏ in terms of πΈ, π, and π? [A] πΏ = 7πΈ β π β 3π [B] πΏ = (π + 3π β πΈ)/7 [C] πΏ = β7πΈ + π + 3π [D] πΏ = (π + 3π + πΈ)/ 7.

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### Video Transcript

The formula πΈ equals π plus three π plus πΏ over seven is often used by teachers to compute the estimated time needed by students to complete homework, πΈ, where π the shortest completion time, πΏ the longest, and π the most likely. Which of the following correctly gives πΏ in terms of πΈ, π, and π? A) πΏ equals seven πΈ minus π minus three π. B) πΏ equals π plus three π minus πΈ over seven. C) πΏ equals negative seven πΈ plus π plus three π. Or D) πΏ equals π plus three π plus πΈ over seven.

Instead of looking through the answer choices and trying to select which one is correct, the better option is to solve for πΏ ourselves and then line that up with one of the four answer choices. Weβre trying to get πΏ by itself. And to do that, weβll have to get rid of this fraction. So, we multiply both sides of the equation by seven over one. On the right, the sevens cancel out. And youβre left with π plus three π plus πΏ.

Seven over one times πΈ equals seven πΈ. From there, we subtract π from both sides. The πs on the right cancel out. So, we have seven πΈ minus π equals three π plus πΏ. And then, we subtract three π from both sides. On the right, the three πs cancel out. And we have seven πΈ minus π minus three π equals πΏ. If we flip that around, πΏ equals seven πΈ minus π minus three π, which is option A out of the answer choices.