Math Problem Monday - August 20th, 2018 | Mathnasium Livermore, CA

Aug 20, 2018 | Livermore

Lower Elementary
Question: Shana picked blueberries and blackberries. She picked three times as many blueberries as blackberries. If she picked 880 berries altogether how many of each berry did she pick?
Answer: 220 blackberries and 660 blueberries.
Note: Students can use the guess and check method. The other option is that the there are 3 parts blueberries and 1 part blackberries. That is a total of 4 parts. Divide 880 into 4 equal parts. In each part there are 220 berries. So in the one part that is blackberries there are 220 berries.  In the other three parts there are 660 blueberries.

Upper Elementary
Question: Megan is saving money for a vacation. She spends $60 out of every $80 she earns. If she saves $240 each month, how much money does she earn each month?
Answer: $960
Note:  To find out how much money she saves out of every $80 she earns subtract. $80 – $60 = $20. If she saves $240 each month then she saved 12 groups of $20. $240 ÷ $20 = 12. That means she earned 12 groups of $80. $80 x 12 = $960.

Middle School
Question: After spending 2/5 of her money, Shannon earned $450 selling her bike. At this time, the amount of money she had was 3/4 of the amount she had originally. How much money did she have originally?
Answer: $3000
Note: Let x be the original amount Shannon started with.  Since she spent 2/5 of her money that means she has 3/5 left.  That gives 3/5x as the amount of money she has after spending, then she earned $450 for the sale of her bike. That gives a total of 3/5x + 450. This is equal to 3/4 of original amount.
3/5x + 450 = 3/4x. Multiplying the equation by the LCM of (4, 5) = 20 gives 12x + 9000 = 15x.  Solving for x we find x = 3000.

Algebra and Up
Question: The Healthy Cereals company makes a cereal that is a mixture of dried berries and granola. The cereal was originally 1/5 dried berries and Healthy Cereals changed it by adding 3 oz. more dried berries. The final mixture is 1/3 dried berries. How many total ounces of cereal are in the final mixture?
Answer: 18 oz.
Note: Let x = the ounces of cereal in the final mixture, then x – 3 = the ounces of cereal before the extra dried berries are added.   If the initial mixture of cereal is 1/5 berries, then 4/5 of the cereal is granola. That means there are 4/5(x – 3) ounces of granola in the  original mixture.  After adding the dried berries, the fraction of the cereal that is granola is 2/3. That means 2/3(x) ounces of granola are in the final mixture.  Since there is the same amount of granola in the original mixture as in the final mixture.  4/5(x – 3) = 2/3(x). Solving for x we find x = 18.

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