use the additive inverse to find 8.76 - 26.54.
To find the additive inverse of a number, we simply change its sign, so the additive inverse of 8.76 is -8.76.
To solve 8.76 - 26.54 using the additive inverse, we can rewrite the expression as a sum of two numbers, with the second number being the additive inverse of 8.76.
8.76 - 26.54 = 8.76 + (-8.76) - 26.54
Now, we can add the two numbers together.
8.76 + (-8.76) = 0
Therefore,
8.76 - 26.54 = 0 - 26.54 = -26.54
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.(1 point)
Let's assume that it takes x minutes for the two machines to have filled the same number of cans of soup.
Machine 1 fills cans at a rate of 15 per minute, so in x minutes it will have filled 15x cans of soup.
Machine 2 fills cans at a rate of 12 per minute, so in x minutes it will have filled 12x cans of soup.
The equation to represent when the two machines will have filled the same number of cans of soup is:
180 + 15x = 210 + 12x
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.(1 point)
Responses
Let's assume that it takes x hours for the two popcorn machines to have the same amount of popcorn left.
Movie Theatre A sells 3 gallons of popcorn per hour, so in x hours it will have sold 3x gallons of popcorn. Therefore, the amount of popcorn remaining in Movie Theatre A's machine after x hours is 100 - 3x gallons.
Movie Theatre B sells 5 gallons of popcorn per hour, so in x hours it will have sold 5x gallons of popcorn. Therefore, the amount of popcorn remaining in Movie Theatre B's machine after x hours is 150 - 5x gallons.
The equation to represent when the two popcorn machines will have the same amount of popcorn left is:
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.(1 point)
Let's assume it takes x days for the two ice cream machines to have the same amount of ice cream left.
The vanilla ice cream machine sells 20 cups per day, so in x days it will have sold 20x cups of ice cream. Therefore, the amount of ice cream remaining in the vanilla ice cream machine after x days is 180 - 20x cups.
The chocolate ice cream machine sells 16 cups per day, so in x days it will have sold 16x cups of ice cream. Therefore, the amount of ice cream remaining in the chocolate ice cream machine after x days is 140 - 16x cups.
To find when the two machines will have the same amount of ice cream left, we can set the two expressions equal to each other:
180 - 20x = 140 - 16x
Now we can solve the equation:
180 - 140 = -16x + 20x
40 = 4x
x = 10
Therefore, the two machines will have the same amount of ice cream left after 10 days.
Give an equation
The equation to represent when the two ice cream machines will have the same amount of ice cream left is:
180 - 20x = 140 - 16x