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News from Mathnasium of North Alpharetta

Problems of the Week: June 22-July 3

Jul 2, 2020

Word Problem Wednesday: Skills and Talents!

By Mathnasium | July 1, 2020 

Introduction

From playing sports, to winning debates, to creating art, each child has his or her own unique skills and talents. In this week’s word problems, your child will explore some of the math behind using them. And who knows? It may spark ideas for applying math when they practice their own skills and talents!

Go to the next page and read this week’s description with your child. Choose the word problem that’s the right skill level for them and have them give it a try! After they feel they’ve found the answer, visit page 3 for the solution!

It’s Amazing What You Can Do!

Running for class elections, playing sports, and making art all require lots of talent and skill! Practice this week’s word problem for ideas on how you might use math to practice and develop your own special abilities!

Choose the word problem below that’s the right skill level for you. Take your time working it out — and no peeking! We know you can do it! When you feel you’ve found the answer, see the next page to check your solution against ours.


Lower Elementary:
Question: Jake is practicing his tetherball skills. Every time he hits the ball, it takes 6 seconds to swing back around the pole. How many times can Jake hit the ball in 45 seconds?

Upper Elementary:
Question: Deb usually shoots glamour portraits for $26.00, but today they are discounted at 75% off. How much do glamour portraits cost today?

Middle School:
Question: Pedro is running for class president. Right now, 112 of the students in Pedro’s class plan to vote for him. He has 1 opponent and 5 weeks to campaign. If there are 144 students in his class, then how many more students does he need to convince to vote for him in order to win the election?

Algebra and Up:
Question: Rico throws a football into the air. The football’s height above the ground in meters after a given amount of time in seconds t can be found using the function f(t) = –5t2 + 15t + 2. How long does the football stay in the air after Rico throws it? You may use your calculator. Round your answer to the nearest tenth of a second.

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 34, the price of the discounted glamour portraits is 14 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 112 of the votes, so 512 more would bring him up to half, and 1 more than that would win him the election. So, since 512 × 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.