Write an equation and interpret the solution to the following problem: Rental car A has a rate of an initial $100, plus $10 per day. Rental car B has a rate of an initial $50, plus $20 per day. After how many days are the rental car prices equal?(1 point)
Responses
50+20x=100+10x; x=5; after 5 days the prices are equal
50 plus 20 x equals 100 plus 10 x ; x equals 5 ; after 5 days the prices are equal
50x+20=100x+10; x=5; after 5 days the prices are equal
50 x plus 20 equals 100 x plus 10 ; x equals 5 ; after 5 days the prices are equal
50+20x=100x+10; x=1; after 1 day the prices are equal
50 plus 20 x equals 100 x plus 10 ; x equals 1 ; after 1 day the prices are equal
20x−50=10x−100; x=−5; after 5 days the prices are equal
Two machines at a factory are filling cans of soup. One machine has already filled 180 cans of soup, and fills cans at a rate of 15 per minute. The second machine has already filled 210 cans of soup, and fills cans at a rate of 12 per minute. Write an equation to show when the two machines will have filled the same number of cans of soup. Use x as your variable.
ANSWER; 12x+210=15x+180
Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left. Use x as your variable.
Answer: 100−3x=150−5x
An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.
Answer 180−20x=140−16x ; x=10
Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.
Answer 120−7x=150−9x ; x=15
Write an equation and interpret the solution to the following problem: Rental car A has a rate of an initial $100, plus $10 per day. Rental car B has a rate of an initial $50, plus $20 per day. After how many days are the rental car prices equal?
Answer:
50+20x=100+10x; x=5; after 5 days the prices are equal
The correct equation is: 50+20x=100+10x; x=5; after 5 days the prices are equal.
This means that after 5 days, the total cost for both rental cars A and B will be the same.
The correct equation for this problem is:
50 + 20x = 100 + 10x
To interpret the solution, we solve for x:
50 + 20x - 10x = 100
10x = 50
x = 5
Therefore, after 5 days, the prices of rental car A and rental car B are equal.
The equation that represents the problem is: 50 + 20x = 100 + 10x. Let's break this down:
- The term "50" represents the initial cost of rental car B.
- The term "20x" represents the cost per day for rental car B, where "x" is the number of days.
- The term "100" represents the initial cost of rental car A.
- The term "10x" represents the cost per day for rental car A.
To find the number of days at which the rental car prices are equal, we need to solve the equation for "x". Here's how to do it:
1. Start by combining like terms. Group the terms with "x" on one side of the equation and the constant terms on the other side:
50 + 20x - 10x = 100
Simplify: 50 + 10x = 100
2. Subtract 50 from both sides of the equation to isolate "10x":
50 + 10x - 50 = 100 - 50
Simplify: 10x = 50
3. Divide both sides of the equation by 10 to solve for "x":
10x/10 = 50/10
Simplify: x = 5
Therefore, the solution to the equation is x = 5. This means that after 5 days, the prices of rental cars A and B will be equal.