A basket with 25 similar balls has a mass of 10.3 kg. The same basket with

10 similar balls has a mass of 4.45 kg. What is the mass of the box?

Give your answer in grams.

550 grams

Step-by-step explanation:

From the given knowledge we can set up 2 equations:

25x + y = 10.3

10x + y = 4.45

where x represents the amount of balls, and y represents the weight of the basket.

We can solve one equation for y and then plug that into the other equation.

Solve 25x + y = 10.3 for y:

25 x + y = 10.3

25x + y + (-25x) = 10.3 + (-25x) (Add - 25x to both sides)

y = - 25x + 10.3

We can plug in this value of y into the other equation and solve for y

Substitute-25x+10.3 for y in 10x + y = 4.45:

10x + y = 4.45

10x + (-25x) + 10.3 = 4.45

-15x + 10.3 = 4.45 (Simplify both sides of the equation)

-15x + 10.3 + (-10.3) = 4.45 + (-10.3) (Add - 10.3 to both sides)

-15x = - 5.85 (Divide both sides by - 15)

x=0.39

Now we know what the weight of each ball is. We just need to substitute. 39 for x to find y to get the weight of the basket.

Substitute 0.39 for x in y = - 25x + 10.3:

y = - 25 x + 10.3

y = (-25) (0.39) + 10.3

y = 0.55 (Simplify both sides of the equation)

So the basket weight. 55kg, or 550 grams

10.3 kg + 4.45 kg = 14750