Question

Patricia had less than nine dollars to spend when she went to the grocery store. She bought 1 pound of tomatoes and wanted to spend the rest of her money on potatoes. 1 pound of tomatoes cost $2.40 and 1 pound of potatoes cost $2.20 .

Part A: Write an inequality to show how many pounds of potatoes,x, Patrica can buy.
Part B: Solve the inequality from Part A to find how many pounds of potatoes Patricia can buy.

Answer 1

Part A: 2.40 +2.20x ≤ 9.00

Part B: x ≤ 3; Patricia can buy 3 pounds of potatoes or less

Explanation:

Part A. The total amount Patricia can spend at the grocery store will be at most $9.00. This amount includes the amount spent on tomatoes ($2.40) and the amount spent on potatoes ($2.20x). The amount spent on potatoes is $2.20 for each of the x pounds she want to buy, so will be the product of 2.20 and x.

The inequality is ...

2.40 + 2.20x ≤ 9.00 . . . . . the total of Patricia's purchases is at most $9.

__

Part B. The inequality is solved in basically the same way it would be solved if it were an equation.

2.20x ≤ 6.60 . . . . . subtract 2.40

x ≤ 3 . . . . . . . . . . . . divide by 2.20. (This number is positive, so we keep the sense of the comparison as it is.)

Patricia can buy at most 3 pounds of potatoes.