Algebra Standards

Question

Two days ago, Neil was assigned a set of problems to solve. Today he solved the final three. Yesterday he solved half of those then remaining plus half a problem. The first day he solved half of those assigned plus half a problem. How many problems were in the assigned set?

Answer 1

Let X = problems assigned

first day: he solved X/2 + 1/2 a problem

2nd day: he solved 1/2 (X - X/2 - 1/2) + 1/2 = 1/2 (X/2 - 1/2) = X/4 - 1/4 + 1/2 = X/4 +1/4

last day: he solved 3

add them up to = X

X/2 + 1/2 + X/4 + 1/4 + 3 = 3X/4 + 3/4 + 3 = 3X/4 + 15/4

that sum = X

3X/4 + 15/4 = X

multiply through by 4

3X + 15 = 4X

subtract 3X from both sides to get

15 = X

X=15