The formula 𝐸 equals 𝑆 plus three 𝑀 plus 𝐿 over seven is often used by teachers to compute the estimated time needed by students to complete homework, 𝐸, where 𝑆 the shortest completion time, 𝐿 the longest, and 𝑀 the most likely. Which of the following correctly gives 𝐿 in terms of 𝐸, 𝑆, and 𝑀? A) 𝐿 equals seven 𝐸 minus 𝑆 minus three 𝑀. B) 𝐿 equals 𝑆 plus three 𝑀 minus 𝐸 over seven. C) 𝐿 equals negative seven 𝐸 plus 𝑆 plus three 𝑀. Or D) 𝐿 equals 𝑆 plus three 𝑀 plus 𝐸 over seven.
Instead of looking through the answer choices and trying to select which one is correct, the better option is to solve for 𝐿 ourselves and then line that up with one of the four answer choices. We’re trying to get 𝐿 by itself. And to do that, we’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 you’re left with 𝑆 plus three 𝑀 plus 𝐿.
Seven over one times 𝐸 equals seven 𝐸. From there, we subtract 𝑆 from both sides. The 𝑆s on the right cancel out. So, we have seven 𝐸 minus 𝑆 equals three 𝑀 plus 𝐿. And then, we subtract three 𝑀 from both sides. On the right, the three 𝑀s cancel out. And we have seven 𝐸 minus 𝑆 minus three 𝑀 equals 𝐿. If we flip that around, 𝐿 equals seven 𝐸 minus 𝑆 minus three 𝑀, which is option A out of the answer choices.