Task# Coupon versus discount

Illustrative MathematicsVaries

This task involves solving equations with rational coefficients, and requires students to use the distributive law ('combine like terms'). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented. A somewhat less directed version of this question might simply ask students which discount they'd prefer. After their intuition or calculations show that the answer depends on the price, a further probe asking them to delineate how it depends on the price would lead them to set up and solve the same equation.