Answers to Problems of the Week - April 26 to May 1

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up.

Lower Elementary:

Question: Stevie practices playing her violin for 30 minutes each weekday and 45 minutes each Saturday and Sunday. How much time does Stevie spend practicing each week?

Answer:  4 hours

Solution: Stevie practices for 30 minutes, 5 times. That’s 150 minutes or 2¹/₂ hours over the week. On weekends, she practices for 45 minutes, twice. That’s 90 minutes or 1¹/₂ hours. Over the course of the whole week, Stevie practices for 2¹/₂ + 1¹/₂ = 4 hours.

Upper Elementary: 

Question: An orchestra has 12 first violins, 10 second violins, 8 violas, 8 cellos, and 6 double basses. Each instrument has 4 strings. How many strings are there in the full orchestra?

Answer:  176 strings

Solution:  There are 12 + 10 + 8 + 8 + 6 = 44 instruments in the orchestra. If each instrument has 4 strings, then there are 44 × 4 = 176 strings.

Middle School: 

Question: Grace is saving up to buy a guitar. Her grandmother will give her an additional 75¢ for each dollar that Grace saves. If Grace saves $20 a month for 6 months, how much money does she have to spend on the guitar?

Answer:  $210

Solution:  Grace saves $20 × 6 = $120. Her grandmother gives her an additional 120 × 75¢ = $90. So, Grace has $120 + $90 = $210 to spend on a guitar.

 Algebra and Up:

Question: Ten voice lessons and 5 piano lessons cost $368.75. Five piano lessons and 3 voice lessons cost $176.25. How much does a voice lesson cost?

Answer:  $27.50

Solution:  We can solve this system of equations problem with the elimination method. If v is the cost of a voice lesson and p is the cost of a piano lesson, then we know that 10v + 5p = 368.75 and 3v + 5p = 176.25. Notice that we have 5p in both equations, so we can subtract one whole equation from the other to leave us with one variable to solve for. If we subtract the smaller number of lessons, we’re left with 7v = 192.5. Therefore, a voice lesson costs $192.50 ÷ 7 = $27.50.

Challenge problem to take home. 20 points for the correct answer. 

Using the following rules:

• you can start at any intersection on the figure
• you cannot lift your writing tool once you start tracing
• you cannot trace over any segment more than once,

Can you trace the entire figure below?