A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side measuring b yards and the adjacent side measuring a yards. A’Leila knows that
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Write two different expressions giving the perimeter of the donkey’s pen.
Expression 1: The perimeter of the pen can be calculated by adding up all the sides. In this case, we have two sides measuring b yards and two sides measuring a yards. Therefore, the perimeter can be expressed as: P = 2b + 2a
Expression 2: Alternatively, we can combine the sides to form a single equation. Starting with the length of the pen being b yards and the width being a yards, we can calculate the perimeter by adding the length of each side: P = b + a + b + a. Simplifying this expression gives: P = 2b + 2a.
Both expressions (P = 2b + 2a and P = b + a + b + a) represent the perimeter of the donkey's pen.
Add a fourth row to the table showing the population information for the town of Concord. Concord’s population as of the last census was p people; for its percentage change, choose a negative integer not divisible by two. Write two expressions showing the current estimated population of Concord in terms of p.
Population | Percentage Change | Current Estimated Population in Terms of p
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Town A (a) | 10% | p + 0.1p = 1.1p
Town B (b) | -5% | p - 0.05p = 0.95p
Town C (c) | 2% | p + 0.02p = 1.02p
Concord (p) | -7 | p - 7
Expression 1: The current estimated population of Concord can be obtained by subtracting 7 from the last census population p: p - 7.
Expression 2: Another way to express the current estimated population of Concord in terms of p is by multiplying p by the percentage change in decimal form (since the change is negative): p * (-0.07) = -0.07p.