Equivalent expressions underlined areas need explanations including summary

when working with percentages, be sure to di inguish between the phrase "increase (or decrease) by" and the phrase "increase (or decrease) to" in the problem. These two phrases do not mean the same thing. Example: A property on York Street has an original value of y. and a nearby property on Zion has an original value of 1. Write the increased value of each property in terms of y and 1, respectively. increases by 300% increased on 300% 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, 1. The new property value is 300% of given by this expression: y + 300%(y). z, or 300%(2). Simplify the expression and recognize that 300% is Simplify the expression. recognizing that 300% is the the same as w. same as w. 100 100 + 300%(y) \" + y 300 y _ y 100 y 300%(2) = m2 = y + 3y Increasing by 300% is the same as Increasing '0 300% 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 expresslons. Example: At the souvenir shop, Theo buys k key chains and p photo frames where 77 , 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 ofk and p? l: Represent the total cost In two ways: I, 1.) Find the cost of each item and add them up to nd the total cost. The cost of k key chains ls k dollars. The cost of p photo frames is p dollars. The cost of one T-shirt is 5 Total cost = k + p + 2.) Another way to nd the total cost is by multiplying $2.49 bythe total numberof 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-shlrt, $ Total cost = (k + p) o / Check for equivalence of these two expressions by rewriting the first expression to match the second. Use the Distributive Property to carry out the factorization. k+ pi _(k+p)+ . Remember that representing a scenario using different expressions does not change the result of the scenarlo as long as the expressions are Summary How can you prove that two expresslons are equivalent? Is there more than one way