Students participated in an online survey. The survey revealed that, for every one person who’s favorite color was purple, there were 3 people whose favorite color was red, and 9 whose favorite color was blue. There were 162 students whose favorite color was red. How many students preferred purple, and how many preferred blue?

A80-foot piece of siding is cut into three pieces so that the second piece is four times four times as long as the first piece and the third piece is five times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces.

Which of the following is the best first step in solving the equation below? 4+2㏒³x=17

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?