12. A shipment of TV sets, some weighing 30 kg each and the other weighing 50 kg each, has a total weight of 880 kg. If there are 20 TV sets all together, how many weigh 50 kg and how many weigh 30 kg?

Answer 1

Let's use algebra to solve this problem.

Let x be the number of TV sets that weigh 30 kg, and y be the number of TV sets that weigh 50 kg.

From the problem, we know that:

- x + y = 20 (since there are 20 TV sets altogether)
- 30x + 50y = 880 (since the total weight of the shipment is 880 kg)

Now we have two equations with two unknowns, so we can solve for x and y.

One way to do this is to use the first equation to solve for one of the variables in terms of the other:

x + y = 20

x = 20 - y

Then we can substitute that expression for x into the second equation:

30x + 50y = 880

30(20 - y) + 50y = 880

600 - 30y + 50y = 880

20y = 280

y = 14

So there are 14 TV sets that weigh 50 kg. To find the number that weigh 30 kg, we can substitute y = 14 back into x + y = 20:

x + 14 = 20

x = 6

So there are 6 TV sets that weigh 30 kg.

Therefore, the answer is:

- 14 TV sets weigh 50 kg
- 6 TV sets weigh 30 kg