# Solutions

Fantastic job on today’s word problem! Are you ready to check your answer? Look below to see if your solution matches ours.

**Lower Elementary:***Answer: *8 times*Solution: *If we count up by 6s from 0, we find each second mark when Jake hits the ball. Jake hits the ball at 0, 6, 12, 18, 24, 30, 36, and 42 seconds. The next time he would hit the ball would be at 48 seconds, which is more than 45 seconds. So, if we count up the times that Jake hits the ball, we find that he can hit it 8 times.

**Upper Elementary:***Answer: *$6.50*Solution: *Since 75% is the same as ^{3}⁄_{4}, the price of the discounted glamour portraits is ^{1}⁄_{4} the original price. So, the glamour portraits cost $26.00 ÷ 4 = $6.50.

**Middle School:***Answer: *61 students*Solution: *Pedro has one opponent, so he needs more than half of the students to vote for him in order to win. He already has ^{1}⁄_{12} of the votes, so ^{5}⁄_{12} more would bring him up to half, and 1 more than that would win him the election. So, since ^{5}⁄_{12} × 144 = 60, he would need 60 + 1 = 61 more votes to win.

**Algebra and Up:***Answer: *3.1 seconds*Solution: *To find the amount of time the ball stays in the air, we find the values of t that put the ball 0 feet above the ground by solving for f(t) = 0. We can use the quadratic formula and our calculators to find that when –5t2 + 15t + 2 = 0, t can be either a negative value or ~3.1279… seconds. So, the ball is in the air for approximately 3.1 seconds.