Solve the problem by writing and solving a suitalble system

Solve the problem by writing and solving a suitalble system of equations.

Factories A and B sent rice to stores 1 and 2. A sent 10 loads and B sent 22. Store used 17 loads and store 2 used 15. It cost $200 to ship from A to 1, $350 from A to 2, $300 from B to 1, and $250 from B to 2. $7,850 was spent. How many loads went where?

Solution

Let A to 1 be a1 and A to 2 be a2; Let b to 1 be b1 and A to 2 be b2;

A1 + a2 = 10 -----1

B1+b2 = 22-----2

A1+b1 = 15 ------3

A2+b2 = 17 ----4

200a1 + 300b1 + 350a2+ 250b2 = 7750

Writing everything in a1 terms we have

200a1 + 300 (15-a1) + 350 (10-a1) + 250 (17-10+a1) = 7750

200a1 – 300a1 – 350a1 + 250a1 + 4500+3500+1750 = 7750

200a1 = 2000

A1 = 10

A2 = 0

B1 = 5

B2 = 17

So, the final answer is :

10 from A to 1

0 from, A to 2

5 from B to 1

17 from B to 2