The mass of a box with 6 tennis balls is 2 kg 40 g. The same box with 10 tennis balls is 3 kg 160 g. What is the mass of the empty box?
well, the extra 4 balls added 3.160-2.040 = 1.12g
Now you know how much each ball weighs, so you can figure the mass of the box.
A box filled with 38 identical balls had a mass of 2.13kg.When 26 balls were removed, the total mass of the box and remaining balls was 0.96 Find the mass of the box when it was empty
Thanks
To find the mass of the empty box, we need to subtract the combined mass of the tennis balls from the total mass of the box.
Let's begin by finding the mass of one tennis ball. We can do this by subtracting the mass of the empty box from the total mass with 6 tennis balls.
Total mass with 6 tennis balls = 2 kg 40 g
Empty box = ?
Mass of 6 tennis balls = Total mass with 6 tennis balls - Empty box
Mass of 6 tennis balls = 2 kg 40 g - Empty box
Next, let's find the mass of one tennis ball by dividing the mass of 6 tennis balls by 6.
Mass of 1 tennis ball = (2 kg 40 g - Empty box) / 6
Similarly, we can find the mass of 1 tennis ball when there are 10 tennis balls.
Total mass with 10 tennis balls = 3 kg 160 g
Empty box = ?
Mass of 10 tennis balls = Total mass with 10 tennis balls - Empty box
Mass of 10 tennis balls = 3 kg 160 g - Empty box
Now, let's find the mass of one tennis ball by dividing the mass of 10 tennis balls by 10.
Mass of 1 tennis ball = (3 kg 160 g - Empty box) / 10
Since both expressions represent the mass of one tennis ball, we can set them equal to each other.
(2 kg 40 g - Empty box) / 6 = (3 kg 160 g - Empty box) / 10
Now, we can solve this equation to find the mass of the empty box. Let's simplify the equation first.
Multiply both sides of the equation by 60 to eliminate the denominators.
60 * [(2 kg 40 g - Empty box) / 6] = 60 * [(3 kg 160 g - Empty box) / 10]
Simplify the expression.
(20 * 2 kg 40 g - 20 * Empty box) = (6 * 3 kg 160 g - 6 * Empty box)
Now, convert the masses to grams for easier calculations.
(20 * 2040 g - 20 * Empty box) = (6 * 3160 g - 6 * Empty box)
Multiply within parentheses.
(40800 g - 20 * Empty box) = (18960 g - 6 * Empty box)
Combine like terms.
40800 g - 20 * Empty box = 18960 g - 6 * Empty box
Move the terms with Empty box to one side and the constant terms to the other side.
20 * Empty box - 6 * Empty box = 40800 g - 18960 g
Simplify the equation.
14 * Empty box = 21840 g
Divide both sides of the equation by 14.
Empty box = 21840 g / 14
Empty box ≈ 1560 g
Therefore, the mass of the empty box is approximately 1560 grams.