# Problems of the Week: June 15-19

Jun 17, 2020 | North Alpharetta

Has your child ever counted the minutes until they were done with their studies and could finally go play? This week’s word problems are all about after school because, from saving allowance for that favorite video game to selling chocolates, we know that math can make that special time of day all the more enjoyable!

# Isn’t Free Time After School Great?

After a busy day of studying, it’s finally time to play games and spend quality time with people we care about! Don’t you agree that there’s something special about free time after school? This week’s word problems are about some of the little things that make after-school time so great!

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: Kylie and Layla get on a school bus at 3:15 pm. At 3:23 pm, Layla tells Kylie that they are halfway to her house. How long does it take to get from the school to Layla’s house?

Upper Elementary:
Question: Alice is saving up for a video game that costs \$45.00. She gets \$20.00 every Monday in allowance, but she spends \$15.00 each week on lunch at school. How many weeks will it take for Alice to save up for the video game?

Middle School:
Question: Owen can’t remember the address number of his friend’s house, but he does remember noticing that all four of the digits were even, that they were in order from least to greatest, and that the first two digits form a number with half the value as the number formed by the last two digits. How many possible street address numbers are there with the details Owen remembers?

Algebra and Up:
Question: Bailey sells 21 more chocolate bars than Carlos. Carlos sells 2.5 times as many chocolate bars as Devon. Devon sells as many chocolate bars as Ella. Ella sells a quarter as many chocolate bars as Fran. Fran sells 1 fewer chocolate bars than Ginny. Rewrite each statement into a system of equations.

# Solutions

Lower Elementary:
Solution: From 3:15 pm to 3:23 pm is 23 – 15 = 8 minutes. Since half of the trip from school to Layla’s house takes 8 minutes, that means that the whole trip takes that amount of time doubled. So, the whole trip from school to Layla’s house is 8 + 8 = 16 minutes.

Upper Elementary:
Solution: Each week, Alice gets \$20.00 and spends \$15.00. So, she can save \$20.00 – \$15.00 = \$5.00 per week. She needs \$45.00 to buy the video game, so she can save up that amount in \$45.00 ÷ \$5.00 per week = 9 weeks.

Middle School:
Answer: 3 possibilities: 2244, 2448, and 4488
Solution: Since all the digits have to be even, only 2s, 4s, and 8s can appear in the address number — 6 cannot appear in the address because halving or doubling it would cause an odd digit. So, 22, 24, and 44 can all can be doubled to make a number whose digits are in the set of usable digits. That means 2244, 2448, and 4488 are the possible numbers.

Algebra and Up: