The Department of Natural Resources (DNR) is estimating the deer population in Twin Pines County. Several months ago, DNR rangers captured, tagged, and then released 108 deer. Recently, DNR rangers captured 54 deer in the county and found that 36 of them had been tagged in the earlier capture. The DNR estimates the deer population in the county using the proportion below. What is the DNR estimate of the deer population in the county?

$$ \frac{\text{tagged dear in capture 1}}{\text{deer population}} = \frac{\text{tagged deer in capture 2}}{\text{deer in capture 2}} $$

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Using the proportion given,

$$ \frac{\text{tagged dear in capture 1}}{\text{deer population}} = \frac{\text{tagged deer in capture 2}}{\text{deer in capture 2}} $$ $$ \frac{\text{108}}{\text{deer population}} = \frac{\text{36}}{\text{54}} $$ $$ \text{deer population} = \frac{(108)(54)}{36} $$ $$ \text{deer population} = \boxed{162} $$