Math Problem Monday - June 7th, 2021 | Mathnasium Livermore, CA

Lower Elementary:
Question: On Tiffany’s first birthday, her grandmother gave her 1¢. On Tiffany’s second birthday, her grandmother gave her 2¢. On Tiffany’s third birthday, her grandmother gave her 4¢. For Tiffany’s fourth birthday, her grandmother gave her 8¢. If this pattern continues, how much money will Tiffany receive from her grandmother on her seventh birthday?
Answer: 64¢
Solution: The pattern from the first four birthdays is 1, 2, 4, 8. Each birthday, Tiffany’s grandmother doubles the amount from the previous year. So on her fifth birthday she receives 16¢. On her sixth birthday she receives 32¢. On her seventh birthday she receives 64¢.

Upper Elementary:
Question: A cake recipe calls for a teaspoon of cinnamon, 1 1/2 cups of flour, 1 cup of sugar, 2/3 cups of milk, 1/2 cup of water, and 1/6 a cup of oil. How much total liquid is in the mix?
Answer: 1 1/3 cups
Solution: The liquids that are used in the mix are milk, water, and oil. So we add 2/3 + 1/2 + 1/6 to find the total amount of liquid. In order to add fractions, they all need to have the same name. The common name is sixths.
2/3 = 4/6
1/2 = 3/6
1/6 = 1/6
4/6 + 3/6 + 1/6 = 8/6 = 4/3 = 1 1/3 cups of liquid are in the mix.

Middle School:
Question: 2 1/3 cups of rice can serve 5 people. How many cups of rice are needed to serve 9 people?
Answer: 4 1/5 cups
Solution: One way to solve this problem is to set up a proportion. Let n be the cups of rice needed to serve 9 people. If we set up the proportion of rice to people, we have:
^{2 1/3 cups} / _{5 people} = ^{n cups} / _{9 people}
We can cross multiply to solve for n
2 1/3 × 9 = 5n
(2 × 9 + 1/3 × 9) = 5n To multiply a mixed number by a whole number, multiply the two whole number and the whole number with the fraction. Then add the two products.
18 + 3 = 5n
21 = 5n
21/5 = 4 1/5 = n
We need 4 1/5 cups of rice to serve 9 people.

Algebra and Up:
Question: Solve for x: 2^(4x+20)= 4^(4x–6)
Answer: x = 8
Solution: One way to solve this problem is to change the problem so both sides have the same base. Factoring the exponent on each side, we have:
2^(4x+20)=4^(4x–6)
2^4(x+5) = 4^2(2x–3)
16^(x+5)=16^(2x–3)
Since both bases are the same, in order for the equation to be “in balance”, the exponents have to be equal.
x + 5 = 2x – 3
–x = – 8
x = 8