Math Problem Monday - December 12th, 2022 | Mathnasium Livermore, CA

Dec 12, 2022 | Livermore

Lower Elementary:
Question: Ryan and Hannah built a lot of snowmen. Five of the snowmen were made with 3 snowballs and four of the snowmen were made with 2 snowballs. How many total snowballs were used to make the snowmen?
Answer: 23 snowballs
Solution: Since five snowmen are made with three snowballs, we can count by 5, three times to get the number of snowballs. 5, 10, 15. 15 snowballs were used to make those snowmen. Four snowmen are made with 2 snowballs, so we count by 4, two times to get the number of snowballs. 4, 8. 8 snowballs were used to make those snowmen. The total number of snowballs used are 15 + 8 = 23 snowballs.

flourUpper Elementary:
Question: A container has 2 cups of flour. Alex used 3/4 of a cup to make pancakes and then used 2/5 of a cup to make strawberry shortcake. How much flour does Alex have left?
Answer: 17/20
Solution: After using the flour for the pancakes, there is 2 – 3/4 = 1 1/4 cups of flour left. After making the strawberry shortcake, there is 1 1/4 – 2/5 = 1 5/20 – 8/20 = 25/20 – 8/20 = 17/20 cups of flour left.

treeMiddle School:
Question: Justine is 48 inches tall and casts a 5–foot shadow. The tree next to Justine is 10 feet tall. How long is the shadow that the tree casts in feet?
Answer: 12.5 feet
Solution: Since Justine’s height is in inches and everything else is in feet, we need to convert her height first. Since there are 12 inches in a foot, Justine is 48 ÷ 12 = 4 feet. To find the length of the shadow of the tree, we set up a proportion. If we let x be the length of the tree’s shadow, we have 4 / 5 = 10 / x. Cross multiply and we get 4x = 50, which means that x = 12.5. So the tree casts a 12.5-foot shadow.

squarecircleAlgebra and Up:
Question: A square is inscribed in a circle. If the radius of the circle is 4 inches, what is the area of the square?
Answer: 32 square inches
Solution: Since the square is inscribed in the circle, the diameter of the circle is the same as the diagonal of the square. The radius is 4 inches, that means the diameter is 8 inches. Because the diagonal of a square can make a right triangle, we can use the Pythagorean Theorem to find the side lengths. Since it is a square, the side lengths are the same, so we have a2 + a2 = 82
Simplify both sides.
2a2 = 64
Divide both sides by 2.
a2 = 32
Take the square root of both sides.
a = sqrt(32)
So the side lengths of the square are sqrt(32). The area is the side length squared, so the area of the square is sqrt(32) • sqrt(32) = 32 square inches.