Read the information carefully and answer the question below. There are three companies X, Y, and Z. The total number of type A pencils manufactured i...

Read the information carefully and answer the question below.

There are three companies X, Y, and Z. The total number of type A pencils manufactured is 40% less than the total number of type B pencils manufactured by all three companies combined. The ratio of the total number of type B pencils manufactured by Z to the total number of type B pencils manufactured by all three companies is 3 : 10. The number of type A pencils manufactured by X is equal to the total number of pencils manufactured by Y. The number of type A pencils manufactured by Z and Y are equal. The total number of pencils manufactured by X is half of the total number of pencils manufactured by all three companies together.

Note: Total pencils manufactured by any company = (type A + type B) pencils manufactured.

Total number of pencils manufactured by company M is equal to four times the total type A pencils manufactured by X and Z together. If the difference between the total pencils manufactured by M and the total type B pencils manufactured by all three companies is 2000, then find the total number of pencils manufactured by all three companies.