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?
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