In a factory, Machine A was turned on first and it produced 229 dumplings. Then Machine A and Machine B were turned on at the same time to continue production. For every 3 dumplings Machine A produced, Machine B produced 6 dumplings. Machine B produced 51 less than
12 of the total number of dumplings produced. How many dumplings were produced altogether?
| |
Make u the same
(1) x 2 = (3) |
Machine A
(1) |
Machine B
(2) |
Make u the same
(2) x 1 = (4) |
Total |
| Before |
458 |
229 |
0 |
0 |
|
| Change |
+ 6 u |
+ 3 u |
+ 6 u |
+ 6 u |
|
| After |
2 p + 102 |
1 p + 51 |
1 p - 51 |
1 p - 51 |
2 p |
From (3)
458 + 6 u = 2 p + 102
6 u = 2 p + 102 - 458
6 u = 2 p - 356
From (4)
0 + 6 u = 1 p - 51
6 u = 1 p - 51
(3) = (4)
2 p - 356 = 1 p - 51
2 p - 1 p = 356 - 51
1 p = 305
Number of dumplings that were produced altogether
= 2 p
= 2 x 305
= 610
Answer(s): 610
