Lower Elementary:
Question: Brian is decorating Easter eggs. The first egg is colored blue and has a star sticker. The second egg is colored yellow and has a star sticker. The third egg is colored red and has a star sticker. The fourth egg is colored blue and has a heart sticker. The fifth egg is colored yellow and has a heart sticker. The sixth egg is colored red and has a heart sticker. The seventh egg is colored blue and has a star sticker. If this pattern continues, what will the 14th egg be?
Answer: Yellow with a star sticker
Solution: We have 2 different patterns going on: egg color and sticker. Let’s start with the color. The color goes blue, yellow, red, blue, yellow, red, blue. This means that the eighth egg is yellow, the ninth egg is red, the tenth egg is blue, the eleventh egg is yellow, the twelfth egg is red, and the thirteenth egg is blue, making the fourteenth egg is yellow. The stickers go star, star, star, heart, heart, heart, star. This means the eighth egg has a star sticker, the ninth egg has a star sticker, the tenth egg has a heart sticker, the eleventh egg has a heart sticker, the twelfth egg has a heart sticker, the thirteenth egg has a star sticker, and the fourteenth egg has a star sticker. So, the 14th egg is yellow and has a star sticker.
Upper Elementary:
Question: Megan went on an Easter egg hunt. Half of the eggs she found were blue, 1/6 of the eggs she found were green, and the remaining 6 eggs were yellow. How many total eggs did Megan find?
Answer: 18 eggs
Solution: First we need to find the fractional part of the eggs Megan found that are yellow. To find one part, take the whole and subtract the sum of the other parts. 1 whole – half – 1/6 = 1 – 1/2 – 1/6. In order to subtract the fractions, they need to have the same denominator, or the same name. 1 – 3/6 – 1/6 = 2/6 = 1/3. 1/3 of the total eggs are yellow. We know that she found 6 yellow eggs and that yellow eggs represent 1/3 of the total eggs Megan found. So, we need to find 1/3 of what number is 6. 1/3 of 18 is 6. So, Megan found 18 eggs in the Easter egg hunt.
Middle School:
Question: Vivian wants to buy 7 chocolate bunnies. The store sells 4 chocolate bunnies for $12.80. How much do 7 chocolate bunnies cost?
Answer: $22.40
Solution: One way to solve this problem is to find the unit price of the chocolate bunnies and then find the cost of 7 chocolate bunnies. We know the cost of 4 chocolate bunnies, so to find the cost of 1 chocolate bunny, divide the cost by 4. 12.80 ÷ 4 = 3.20. One chocolate bunny costs $3.20. To find the cost of 7 chocolate bunnies, multiply the unit price by 7. $3.20 × 7 = $22.40. 7 chocolate bunnies cost $22.40.
Algebra and Up:
Question: Harold is making colored eggs for Easter and needs to make a color dye mixture that consists of water and 15% vinegar. He has 150mL of a mixture that is 20% vinegar. How much water does Harold need to add to make a mixture that is 15% vinegar?
Answer: 50mL
Solution: Currently we have a mixture that is 150mL and is 20% vinegar. We need to add enough water so that the solution is 15% vinegar. Notice that the amount of vinegar remains the same; we are only adding water. So, let’s find out how many milliliters of vinegar there are in the mixture. 20% of 150 is 30, so there are 30mL of vinegar in the solution. Now, let’s set up a ratio. Let x be the amount of water we are adding to the solution.
amount of vinegar / total amount of mixture = percent vinegar in mixture
30mL/(150mL + x) = 0.15
Cross multiply. Recall that 0.15 is the same as 0.15/1.
30(1) = 0.15(150 + x)
Multiply.
30 = 22.5 + 0.15x
Subtract 22.5 from both sides.
7.5 = 0.15x
Divide by 0.15.
50 = x
So, Harold needs to add 50mL of water to the solution to make a mixture that is 15% vinegar.
Alternatively, since we are not adding any more vinegar to the mixture, to solve the problem we can figure out 15% of what number is 30. 15% of 200 is 30, so the final solution has 200mL. Since the solution started with 150mL, Harold needs to add 50mL of water to make the solution of water and 15% vinegar.
