I need help on how to do system applications word problems. I just don't get this at all :(
1. The ravens won twice as many games as they lost. They played 96 games. How many games did they win?
2. State college has 620 students. There are 20 more women than men. How many women are there?
x + 2x = 96
3x = 96
x = 32 games lost
x + x + 20 = 620
How would you know how to set it up?
The Ravens lost x games. They won twice as many games -- so it's x + 2x = 96
To solve word problems involving system applications, it's important to understand the information given and translate it into mathematical equations. Here's a step-by-step guide on how to solve the two word problems you've provided:
1. The ravens won twice as many games as they lost. They played 96 games. How many games did they win?
Step 1: Assign variables
Let's say the number of games lost is x. Since the ravens won twice as many games as they lost, the number of games won is 2x.
Step 2: Set up an equation
The total number of games played is the sum of games won (2x) and games lost (x), which equals 96. Therefore:
2x + x = 96
Step 3: Solve the equation
Combine like terms: 3x = 96
Divide both sides by 3: x = 32
Step 4: Find the number of games won
Since the ravens won twice as many games as they lost, multiply the number of games lost (32) by 2:
2 * 32 = 64
Therefore, the ravens won 64 games.
2. State college has 620 students. There are 20 more women than men. How many women are there?
Step 1: Assign variables
Let's say the number of men is x. Since there are 20 more women than men, the number of women would be x + 20.
Step 2: Set up an equation
The total number of students is the sum of men (x) and women (x + 20), which equals 620. Therefore:
x + (x + 20) = 620
Step 3: Solve the equation
Combine like terms: 2x + 20 = 620
Subtract 20 from both sides: 2x = 600
Divide both sides by 2: x = 300
Step 4: Find the number of women
Since there are 20 more women than men, add 20 to the number of men (300):
300 + 20 = 320
Therefore, there are 320 women in State College.