The master planned to produce 24 parts daily, however every day he was producing 15 more parts and 6 days

The master planned to produce 24 parts daily, however every day he was producing 15 more parts and 6 days before the deadline he had already made 21 more parts than planned. How many parts the master planned to make.

Let the number of parts that the master planned to make be x, and the number of days during which he had to make them be t. Then, by the condition of the problem, we can write the following equalities:
24t = x;
(24 +15) (t – 6) = x + 21.
Substitute the x value from the first expression into the second:
(24 +15) (t – 6) = 24t + 21.
Let’s simplify and solve the resulting equation:
24t + 15t – 144 – 90 = 24t + 21;
15t = 21 + 144 + 90;
15t = 255;
t = 255: 15;
t = 17 days the master planned to work.
Now let’s find how many parts he planned to make during this time:
24 * t = 408 parts.
Answer: the master planned to make 408 parts.