Students represent and solve percent decrease problems.
When there is a percent decrease between a starting amount and a final amount, the relationship can be represented by an equation of the form y = kx where y is the final amount, x is the starting amount, and k is the constant of proportionality, which is equal to 1 minus the percent change, p, represented as a decimal: k = 1 – p, so y = (1 – p)x.
The constant of proportionality k has the value it does—a number less than 1—because of the way the distributive property can be used to simplify the expression for the starting amount decreased by a percent of the starting amount: x – x(p) = x(1 – p).
Goals and Learning Objectives
- Determine the unknown amount—either the starting amount, the percent change, or the final amount—in a percent decrease situation when given the other two amounts.
- Make a table to represent a percent decrease problem.
- Write and solve an equation to represent a percent decrease problem.