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Three exercises and several math application problems in a math class
For a project, Party A will work alone for 8 days, Party B will work alone for 12 days, and Party C will work alone for 24 days. Now that Party A and Party B have cooperated for three days, Party A has something to leave. How many days will it take Party B and Party C to complete the project?

Suppose it takes X days for B and C to complete the project, then 3/8+3/12+x/12+x/24 =1.

A worker processes a batch of parts in a certain period of time, 44 pieces a day, 20 pieces less than the specified task and 50 pieces a day, carving 10 pieces more than the specified number of parts and the planned processing days.

Assuming that the number of parts to be machined is x, (x-20)/44=(x+ 10)/50.

Solve x

Substituting (x-20)/44, the number of days of planned processing is obtained.

Party A and Party B are repairing a18km highway. Team a repairs 0.5km more than team b every day, and both teams work for 4 days at the same time to complete the task. How many kilometers does each team need to repair every day?

If Team A repairs X kilometers every day, then 4x+4(x-0.5)= 18.

Party A and Party B produce the same kind of parts, with Party A producing 30 pieces a day and Party B producing 24 pieces a day. When Party B produces such parts for 3 days, Party A starts to work. How many days after Party A works, can the output catch up with Party B?

If the output can catch up after working for x days, then 30x=24(x+3).

A concrete is prepared, and the mass ratio of cement, sand, gravel and water is 1: 3: 10: 4. How many kilograms of various raw materials do you need to prepare 360 kilograms of this concrete?

Let the mass of cement, sand, gravel and water be x kg, 3xkg, 10x kg and 4x kg respectively, then

x+3x+ 10x+4x=360

It is stipulated that the operation process of the new operation symbol * is A * B = 1/3 A- 1/4 B, and 5*(-5) is obtained.

5*(-5)= 1/3 *5 - 1/4 * (-5)=5/3+5/4=2 1 1/ 12