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KATRIN_1 [288]
3 years ago
8

A gym has 2kg and 5kg weights. There are 10 disks in all. The total weight of 2kg and 5kg disks is equal to 29kg. Find the numbe

r of disks of each kind in the gym.
Mathematics
1 answer:
Simora [160]3 years ago
6 0

Answer:

no of 5 kg disks is 3, and no of 2 kg disks is (10-3) i.e. 7

Step-by-step explanation:

Let the no of 2kg disks be a.

Let no of 5 kg disks be b.

2a+5b=29

a+b=10

Using substitution, we have

2(10-b) + 5b=29

20-2b+5b=29

20+3b=29

3b=9

b=3

So no of 5 kg disks is 3, and no of 2 kg disks is (10-3) i.e. 7

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We can use this equation to solve this problem:

<span>t=p+<span>(p⋅r)</span></span>

Where:

t is the total price paid: 58.31 for this problem

p is the price before taxes: What we are solving for in this problem.

r is the tax or VAT rate: 19% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 19% can be written as <span>19100</span> or 0.19.

Substituting and solving for p gives:

<span>58.31=p+<span>(p⋅0.19)</span></span>

<span>58.31=1p+0.19p</span>

<span>58.31=<span>(1+0.19)</span>p</span>

<span>58.31=1.19p</span>

<span><span>58.311.19</span>=<span><span>1.19p</span>1.19</span></span>

<span>49=<span><span>1.19p</span>1.19</span></span>

<span>49=p</span>

<span>p=49</span>

Now, we can find how much the VAT was by taking 19% of 49:

<span>19%×49=0.19×49=9.31</span>

Another was to solve this is to subtract the price without the tax or VAT from the total price giving:

<span>58.31−49=<span>9.31</span></span>

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If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x².  To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.

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