## Task 1 - 310711

A department store received a shipment of red, blue, and green balls, totaling 675 pieces. During a certain period, the following were sold:

half of the red balls, two-thirds of the blue balls, and one-quarter of the green balls.

It turned out that after this, the same number of balls remained for each of the three colors.

Determine from these data,

a) how many balls of each of the three colors were sold during this time.

b) how many balls were still available in total afterward!
The number of balls remaining of each color at the end is $x$. According to the problem statement, this came about as follows:

$x$ red balls were sold, so $2 x$ were delivered,

$2 x$ blue balls were sold, so $3 x$ were delivered, and

$3 x$ green balls were sold, so $4 x$ were delivered.

Thus, the entire delivery consisted of $2 x+3 x+4 x=9 x$ balls; hence $9 x=675, x=75$. Therefore, exactly 75 red, 150 blue, and 225 green balls were sold, and afterwards, a total of $3 \cdot 75=225$ balls remained.