A box filled with 38 identical balls had a mass of 2.13kg.When 26 balls were removed,the total mass of box and the remaining balls was 0.96 kg.Find the mass of the box when it was empty

x + 38b = 2.13

x + (38-26)b = 0.96

now just solve for x.

To solve this problem, let's break it down step by step:

Step 1: Find the mass of the 26 balls that were removed:
Since all the balls are identical, we can assume that each ball has the same mass. Let's call the mass of each ball "m". The mass of the 26 balls removed is then 26m.

Step 2: Find the mass of the remaining 12 balls:
The total mass of the box and the remaining balls after 26 were removed is 0.96 kg. Since we already know the mass of the removed balls (26m), we can write the equation:
(box mass + remaining balls mass) = 0.96 kg
Let's call the mass of the box "M". The mass of the remaining 12 balls is then 12m. Substituting these values into the equation, we get:
(M + 12m) = 0.96 kg

Step 3: Find the total mass of the box with no balls:
If we remove all the balls, the mass of the box itself will remain. So, we need to find the mass of the box when it is empty. Let's call this mass "M_empty".

Step 4: Set up an equation and solve for M_empty:
The mass of the box with no balls (M_empty) is equal to the mass of the box plus the mass of the 38 balls. Therefore, we can set up the equation:
M_empty = M + 38m

Step 5: Combine the equations and solve for M_empty:
Substituting the value of M from Step 2 into the equation from Step 4, we get:
M_empty = (0.96 kg - 12m) + 38m
Simplifying the equation, we have:
M_empty = 0.96 kg + 26m

Now, we need to find the value of "m" in order to determine the mass of the box when it was empty.

Step 6: Find the value of "m":
We are given that the total mass of the box with 38 balls is 2.13 kg. Substituting this into the equation, we get:
2.13 kg = M + 38m

Step 7: Substitute the value of "M" into the equation from Step 6:
From Step 2, we found that M = 0.96 kg - 12m. Substituting this into the equation from Step 6, we have:
2.13 kg = (0.96 kg - 12m) + 38m

Step 8: Simplify and solve for "m":
Expanding the equation, we have:
2.13 kg = 0.96 kg + 26m

Now, isolate the term with "m":
26m = 2.13 kg - 0.96 kg

Subtracting the values on the right side, we get:
26m = 1.17 kg

Finally, divide both sides by 26 to solve for "m":
m = 1.17 kg / 26
m = 0.045 kg

Step 9: Calculate the mass of the box when it was empty:
Substituting the value for "m" into the equation from Step 5, we get:
M_empty = 0.96 kg + 26(0.045 kg)
M_empty = 0.96 kg + 1.17 kg
M_empty = 2.13 kg

Therefore, the mass of the box when it was empty is 2.13 kg.