Math Problem Monday - Feb 19th, 2018 | Mathnasium Livermore, CA

Feb 19, 2018 | Livermore

Lower Elementary
Question: The sum of two number is 35 and the difference of the same two numbers is 13.  What are the two numbers?
Answer: 24 and 11
Note:  Use guess and check method.

Upper Elementary
Question: Ella bought 8 pounds of ground beef.  She used 2 3/4 pounds of ground beef to make chili and another  3 2/5 pounds of ground beef to make hamburgers.  How many pounds of ground beef did she have left?
Answer: 1 17/20 pounds
Note: Ella started with 8 pounds of ground beef.  She first used 2 3/4 pounds so she had (8 – 2 3/4) 5 1/4 pounds left.  Then she used another 3 2/5 pounds so she had (5 1/4 – 3 2/5) 1 13/20 pounds left.  You can also combine the amount of ground beef she used first then subtract it from the 8 pounds of ground beef. 2 3/4 + 3 2/5 = 5 23/20 = 6 3/20.  8 – 6 3/20 = 1 17/20

Middle School
Question: Frank and his little brother were standing outside on a sunny day.  At the same time that Frank’s shadow measures 16.5 feet his brother’s shadow measures 12 feet.  If Frank is 5.5 feet tall, how tall is his little brother?
Answer: 4 feet
Note: This problem can be solved in two ways.
Number sense solution:
Frank is 5.5 feet tall and his shadow is 16.5 feet long.  His shadow is 3 times as long as he is tall, 16.5 ÷ 5.5 = 3.  This means his brother’s shadow is 3 times as long as he is tall.  Since his shadow is 12 feet long then Frank’s little brother is (12 ÷ 3) 4 feet tall.
Algebraic solution:
We can set up the proportion of the ratio of Frank’s height to his shadow’s length and his little brother’s height to his shadow’s length.
5.5/16.5 = x/12
Taking the cross products we have:
16.5x = 66
Dividing both sides by 16.5 we find,
x = 4

Algebra and Up
Question: Let z# mean 6z3 – z2 + 2.  Then what is (x – 4)#?
Answer: 6x3 – 73x2 + 296x – 398
Note:  Using the definition of z#,
(x – 4)# = 6(x – 4)3 – (x – 4)2 + 2
= 6(x – 4)3 – x2 + 8x – 14
= 6x3 – 48x2 + 96x – 24x2 + 192 – 384 – x2 + 8x – 14
= 6x3 – 732 + 296x – 398

Math tutors near

Could not find Center, try again