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A bottle (b) and a cork (c) cost a dollar and a nickel:
b + c = 1.05
The bottle (b) costs a dollar more than the cork (c):
b = c + 1
So we have this:
b + c = 1.05
b = c + 1
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In the second equation the b is already isolated on the left so we can replace b in the first equation with c + 1:
c + 1 + c = 1.05
c + c + 1 = 1.05 | c + c = 2c
2c + 1 = 1.05 | - 1
2c = 0.05 | : 2
c = 0.025
Now we only need to replace c in the second equation by its value to calculate b:
b = 0.025 + 1
b = 1.025