Students represent and solve percent increase problems.
When there is a percent increase 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 plus 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 greater than 1—because of the way the distributive property can be used to simplify the expression for the starting amount increased 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 increase situation when given the other two amounts.
- Make a table to represent a percent increase problem.
- Write and solve an equation to represent a percent increase problem.