Lower Elementary:
Question: Grace received 2 boxes of chocolates. Each box contains 15 pieces of chocolate. If Grace eats 4 pieces, how many does she have left?
Answer: 26 pieces of chocolate.
Solution: To find the total number of pieces Grace started with, double 15. She has 30 pieces of chocolate originally. She ate 4, so subtract 4 from the total. 30 – 4 = 26 pieces of chocolate.
Upper Elementary:
Question: Megan wants to buy 30 Valentine’s Day cards for her friends. The store sells them in packs of 10 for $6.50. If Megan pays with a $20 bill, how much change will she get back?
Answer: 50 cents
Solution: Megan pays $6.50 for every 10 Valentine’s Day cards. Since she wants 30 cards, she will need 3 packs of cards (10 + 10 + 10 = 30). Paying $6.50 for each will be $6.50 + $6.50 + $6.50, or $6.50 × 3. Thirty cards cost $19.50. The amount of change she will receive is 50 cents ($20 – $19.50 = 50 cents).
Middle School:
Question: Kyle is going to pay for a Valentine’s Day dinner. The bill is $85 without tax. Kyle wants to give a 20% tip on the bill before the tax is added. The tax is $5. What is the total amount that Kyle will pay?
Answer: $107
Solution: Algebraic:
Multiply the bill by the tip percent. $85 × 0.2 = $17
Number sense:
20% of a number is the same as 1/5 of a number. 1/5 of 85 is 17, so 20% of $85 is $17
Add the tip and tax to the bill to get the total: $85 + $17 + $5 = $107.
Algebra and Up:
Question: Jordan is going to spend $20 on a bouquet of roses and tulips. The florist sells roses for $4 each and tulips for $3 each. If Jordan purchases 6 flowers, how many of each are purchased?
Answer: 2 roses and 4 tulips
Solution: One way to solve this is to use a system of equations. Let r be the number of roses purchased and let t be the number of tulips purchased. The two equations are:
(1) The whole is equal to the sum of its parts: (number of roses) + (number of tulips) = (number in bouquet): r + t = 6
(2) Total cost: (cost of roses) × (number of roses) + (cost of tulips) × (number of tulips) = (total cost of the bouquet): 4r + 3t = 20
Let’s solve this system of equations using elimination (you can also solve this using other methods such as graphing or substitution).
r + t = 6
4r + 3t = 20
Multiply the top equation by –3:
–3r + –3t = –18
4r + 3t = 20
Add the two equations together (so that the t can cancel):
r = 2
Plug this into equation (1) and solve for t:
2 + t = 6
t = 4
Jordan buys a bouquet of 2 roses and 4 tulips.
