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A gym has 5 kg and 8 kg weights. There are 14 disks in all. The total weight of 5 kg disks 8 kg disks is equal to 100 kg. Find the number of disks of each kind of gym.

 Feb 25, 2020
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Let x be the number of 5 kg weights and y be the number of 8 kg weights. Because there are 14 disks, x+y = 14.

Now, looking to weight; if there are x 5 kg weights, then they weigh 5x kg total. Similarly, the y 8 kg weights weigh 8y kg total.

So, if their total weight is 100 kg, 5x + 8y = 100.

 

From here, you can multiply both sides of the equation 'x+y = 14' 5 to get '5x+5y=70'.

You subtract '5x+5y=70' from '5x+8y=100' to get '3y=30', so dividing by 3 gets us y=10. There are 10 '8 kg' disks.

 

Going back to x+y = 14, we can substitute y=10 to find that x+10 = 14; subtracting 10 from both sides gets us x = 4. There are 4 '5 kg' disks.

 Feb 25, 2020

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