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When working with percentages, be sure to distinguish between the phrase "increase (or decrease) by" and the phrase "increase (or decrease) to" in the problem. These two phrases do not mean the Total cost (k + p) + ame thing. Check for equivalence of these two expressions by rewriting the first expression to match the second. Example: A property on York Street has an original value of y, and a nearby property on Zion has an original Use the Distributive Property to carry out the factorization. value of z. Write the increased value of each property in terms of y and z, respectively. increases by 300% increased to 300% _p +_ ( k + p) + The current value, y, of the York Street property The property on Zion increased to 300% of its increases by 300%%. The new value of the property is original value, z. The new property value is 300%% of Remember that representing a scenario using different expressions does not change the result of the given by this expression: y + 300%[v). z, or 300%%(z). scenario as long as the expressions are Simplify the expression and recognize that 300% is Simplify the expression, recognizing that 300% is the the same as 100' same as 100 300 Summary y + 300%()) =y + 10 > 300% (2)= 300 How can you prove that two expressions are equivalent? Is there more than one way? 100 my + 3y Increasing by 300% is the same as Increasing to 300% is the same as the original value by the original value by _ More Equivalent Expressions Here's a situation involving multiple variables that we can model using equivalent expressions. Example: At the souvenir shop, Theo buys k key chains and p photo frames where each chain and frame costs $2.49. He also buys a T-shirt for $5.99. What is the total cost of Theo's purchases in terms of k and p? Represent the total cost in two ways: C 1.) Find the cost of each item and add them up to find the total cost. The cost of k key chains is k dollars. The cost of p photo frames is p dollars. The cost of one T-shirt is $ Total cost = k + p +_ 2.) Another way to find the total cost is by multiplying $2.49 by the total number of key chains and photo frames (k + p) that Theo bought since both items have the same unit price. Then, complete the expression by adding the cost of the T-shirt, $