Problem 86 - Elementary Algebra

Question

The rulebook of the U.S. Lawn Mower Racing Association describes how to award points. 100 points for registration 100 points for starting a race 100 points for finishing a race 300 points for first place 250 points for second place 200 points for third place 150 points for fourth place 100 points for fifth place Source: www.letsmow.com A lawn mower racer registered for a day of racing. She started and completed three races. She placed fourth in the first race, third in the second race, and first in the final race. Find the total number of points she earned.

Step-by-Step Solution

Answer

1650 points.

Step 1: Points for Registration

Start by calculating the points awarded for registration. According to the rulebook, registering earns 100 points.

Step 2: Points for Starting Races

Next, calculate the points for starting each race. She started three races, and each start earns 100 points. Multiply 100 points by 3 races.

Step 3: Points for Finishing Races

Now calculate the points for finishing each race. She finished all three races, and each finish earns 100 points. Multiply 100 points by 3 races.

Step 4: Points for Placing in Races

Calculate the points based on her placement in each race. For the first race, she placed fourth (150 points). For the second race, she placed third (200 points). For the final race, she placed first (300 points). Sum these points.

Step 5: Total Points

Sum all the points from registration, starting races, finishing races, and placements to get the total points earned.

Key Concepts

point system calculations

In many competitive sports, points are awarded based on various achievements like participating, finishing, or achieving certain ranks in the event. Understanding how to calculate points accurately is crucial for determining the winner. In this lawn mower racing problem, points are assigned for:

• Registration: 100 points
• Starting a race: 100 points per race
• Finishing a race: 100 points per race
• Placing in races: Variable points

Let’s break it down. Our racer participated in three races and registered for the event. This means she will earn:

Registration: 100 points

Starting: 100 points x 3 races = 300 points

Finishing: 100 points x 3 races = 300 points

Then, we look at her rankings. She got fourth place in the first race (150 points), third place in the second race (200 points), and first place in the final race (300 points). Hence, her placing points are:

Fourth place: 150 points

Third place: 200 points

First place: 300 points

Adding all these together, you get the total points she earned.

step-by-step problem solving

Breaking down problems into smaller, sequential steps makes solving complex problems easier. Here's how we'd handle our lawn mower racing problem:

Step 1: Points for Registration

The first step is identifying the points given for registering. According to the rulebook, registration alone earns 100 points.

Step 2: Points for Starting Races

The next step is to calculate how many points are awarded for starting races. She started three races, so you multiply the 100 points per race by 3.

Step 3: Points for Finishing Races

Calculate the points for finishing races by multiplying the 100 points per race by 3 again, because she finished all three races.

Step 4: Points for Placement in Races

Evaluate her placement in each race. She placed fourth in the first, third in the second, and first in the final race, then sum the points for each placement (150, 200, and 300 points, respectively).

Step 5: Total Points

Combine all the points collected from the previous steps (registration, starting, finishing, and placement) to find the total points earned.

elementary algebra

Elementary algebra involves basic mathematical skills like addition, multiplication, and understanding variables. In our problem, we use these skills to calculate the total points a racer earned.

Let's use some algebraic expressions to represent the total points:

Let:
\( R = \text{Registration points} \)
\( S = \text{Starting race points} \)
\( F = \text{Finishing race points} \)
\( P_4 = \text{Points for placing fourth} \)
\( P_3 = \text{Points for placing third} \)
\( P_1 = \text{Points for placing first} \)
The total points: \[ T = R + (S \times 3) + (F \times 3) + P_4 + P_3 + P_1 \]
Plugging in the known values:\[ T = 100 + (100 \times 3) + (100 \times 3) + 150 + 200 + 300 \]
Simplify the expression step-by-step:

\( 100 + 300 + 300 + 150 + 200 + 300 = 1350 \)
Therefore, the racer earned a total of 1350 points. This example illustrates how elementary algebra can be used to systematically approach and solve problems.