Lower Elementary:
Question: Dean is buying strings to fix his guitar. Each string costs $4. He needs to buy two strings. How much change will he receive if he pays $10?
Answer: $2
Solution: First, we need to find the cost of the guitar strings altogether. Each string is $4 and he buys 2 strings. 4 doubled is 8. So, the guitar strings cost $8. If he pays $10, then he will receive $10 – $8 = $2 in change.
Upper Elementary:
Question: A rectangle has a length of 12 inches and a width of 5 inches. A triangle has a base that is 7 inches and two sides that are 10 inches long. The base of the triangle is centered on width of the rectangle. What is the perimeter of this shape?
Answer: 51 inches
Solution: The perimeter is the distance around a shape. So, we need to add the lengths of each side of the shape. We know that the base of the triangle is 7 inches and the width of the rectangle is 5 inches. That means that 7 – 5 = 2 inches of the triangle is not covered by the width of the rectangle. Since the triangle is centered, that means that it extends 1 inch past the rectangle on each side. So, now we add the lengths of each side of the shape.
10 + 10 + 1 + 12 + 5 + 12 + 1 = 20 + 24 + 2 + 5 = 44 + 7 = 51
The perimeter of this shape is 51 inches.
Middle School:
Question: Eddie, Sam, and Jordan worked together to buy speakers for their dance project. Eddie put in $50, Sam put in $75, and Jordan put in $25. They decided to then sell the speakers for $120. How much of the selling price should each person receive so that it is fair?
Answer: Eddie: $40, Sam: $60, Jordan: $20
Solution: To make it fair, each person should receive the fractional part that they put in to buy the speakers. The total amount of the speakers is $150 ($50 + $75 + $25). Eddie paid for 1/3 of the speakers (50/150 = 1/3), Sam paid for 1/2 of the speakers (75/150 = 1/2), and Jordan paid for 1/6 of the speakers (25/150 = 1/6). To find how much each person should receive, find each of the respective fractional parts of $120.
Eddie: 1/3 of $120 = $40
Sam: 1/2 of $120 = $60
Jordan: 1/6 of $120 = $20
Algebra and Up:
Question: The temperature in Fahrenheit of a particular day can be modeled by the equation F(t) = (2 – t)(t – 20) where t is the number of hours after midnight. What is the hottest temperature on this particular day and at what time does it occur?
Answer: 81°F at 11:00am
Solution: If we foil the function, we have that F(t) = –t2 + 22t – 40. Notice that this is the equation of a parabola that opens down since the coefficient if front of t2 is negative. That means that the highest point is at the vertex. One way to find the vertex is to find the hour when it is the hottest first by finding –b/2a. In this problem, b = 22 and a = –1. So,
–b/2a = –22/((2)(–1)) = –22/–2 = 11
So, the hottest temperature happens when t = 11. Since t is the number of hours past midnight, the hottest temperature occurred at 11:00am
To find out what the hottest temperature is, we substitute 11 for t in the function.
F(11) = (2 – 11)(11 – 20) = (–9)(–9) = 81.
The hottest temperature on that day was 81°F.
(925) 292-8854
