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If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three halves of the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?
Detailed Explanation
This word problem requires careful translation. Let’s say t = total current inventory of chairs.
The first sentence states that \(50 + t = \frac{\mathrm{3} }{\mathrm{2}} t\). First solve for the current inventory:
\(50 + t = \frac{\mathrm{3} }{\mathrm{2}} t\)
50 = \(\frac{\mathrm{3t} }{\mathrm{2}}\) - t
\(50 = \frac{\mathrm{1} }{\mathrm{2}}t\)
t = 100.
The manager wants to increase this by 40%. We know that 40% of 100 is 40, so the new inventory will be 140.
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