Lower Elementary
Question: In Los Angeles, California it rained 3 inches on Friday, 4.8 inches on Saturday, and 2 inches on Sunday. During those same days it rained 4 inches, 5 inches, and 6 inches in Miami, Florida. Which city had the most rainfall during the three days? How much more?
Answer: Miami, 5.2 inches
Note: First, add up the inches of rain for both Los Angeles and Miami.
Los Angeles: 3 + 4.8 + 2 = 9.8 inches
Miami: 4 + 5 + 6 = 15inches
We see that Miami had more inches of rain than Los Angeles.
Then subtract the Los Angeles rainfall from the Miami rainfall.
15 – 9.8 = 5.2 inches
Upper Elementary
Question: On a rainy day it takes a car going 35 mph (miles per hour) 180 feet to stop completely after applying the brakes. On a sunny day the same car traveling at the same speed can come to a complete stop in three fourths the distance it takes on a rainy day. How many feet does it take for the car to stop on a sunny day?
Answer: 135 feet
Note: This problem has extra facts. The information that the car is traveling 35 mph is not used in any of the calculations.
In order to solve this problem we need to find ¾ of 180. We start by finding ¼ of 180.
A quarter means half of a half. half of 180 = 90 and half of 90 = 45.
That means ¼ of 180 is equal is 45. Because we are trying to find ¾ of 180 we need to add three 45’s together or multiply 45 by 3 and we get 135 feet.
45 + 45 + 45 = 135
45 x 3 = 135
Middle School:
Question: Jenny spent 1/3 of the money she had on an outfit. She then earned $390.50 from her job. After all of this she had 5/4 the amount of money she originally had. How much money did Jenny have to start with?
Answer: $669.43
Note: : Since we don’t know how much money Jenny started with let’s call that total amount x. We know she spent a third of the money she started with on a new outfit. That means she has 2/3 of the money she started with left.
1 – 1/3 = 3/3 – 1/3 = 2/3. That means the amount of money she now has is (2/3)x.
She earned, $390.50 after buying the outfit. Adding the money she has left over to the money she eared gives an amount equal to five fourths the amount of money she started with.
(2/3)x + 390.50 = (5/4)x
Now solve for x.
390.50 = (5/4)x – (2/3)x
Next, find the least common denominator for 3 and 4, which is 12. Then, subtract.
390.50 = (15/12)x – (8/12)x
390.50 = (7/12)x
Multiply both sides by the reciprocal of (7/12).
390.50 • (12/7) = x
x = $669.43
Algebra and Up
Question: Find the area of the shaded region. (Round answer to the nearest tenth)
Answer: 28.5 units2
Note: Since a part is equal to the whole minus the other part. The area of the shaded region is equal to the area of the circle minus the area of the square. That means we need to find the area of both the circle and the square.
We will start by finding the area of the square. A diagonal of the square is equal to the diameter of the circle. Since the radius of the circle is 5, that means the diameter of the circle is 10. So the diagonal of the square is 10.
The diagonal of the square cuts the square into two isosceles right triangles or 45-45-90 special right triangles. Where the diagonal is the hypotenuse of both triangles. The relationship between the hypotenuse and the a side s is hypotenuse = s√2. Since the hypotenuse is 10, that means
s√2 = 10, and s = 5√2.
The area of the square is found by squaring the side.
Asquare = s2 = (5√2)2 = 25 • 2 = 50 units2
Now we need to find the area of the circle.
Acircle = πr2 = π • 52 = 25π ≈ 78.5 units2
Now subtract the area of the square from the area of the circle.
Acircle – Asquare ≈ 78.5 units2 – 50 units2 = 28.5 units2
