Question

Lance has some tomatoes of which he uses 2 pounds for cooking. He also has some potatoes which are 3 pounds less than twice the initial weight of tomatoes. If he is left with 8 pounds of vegetables in all, how many pounds of tomatoes did he initially have?

Answer 1

To find out how many pounds of tomatoes Lance initially had, we define a variable, set up an equation including the given weights and relationships, and solve for the variable. Solving the equation shows that Lance initially had approximately 4.33 pounds of tomatoes.

Step-by-step explanation:

The question involves solving a two-step algebraic equation to find the initial weight of the tomatoes Lance had.

1. Let T represent the initial weight of Lance's tomatoes in pounds.
2. Lance uses 2 pounds of tomatoes for cooking, so he is left with T - 2 pounds of tomatoes.
3. The weight of the potatoes is 3 pounds less than twice the initial weight of the tomatoes, so it can be represented as 2T - 3 pounds.
4. The total weight of the remaining vegetables is 8 pounds, which is the sum of the remaining tomatoes and the potatoes: (T - 2) + (2T - 3) = 8.
5. Combine like terms to get 3T - 5 = 8.
6. Add 5 to both sides to get 3T = 13.
7. Divide both sides by 3 to find that T = 13/3 or approximately 4.33 pounds.
8. Therefore, Lance initially had approximately 4.33 pounds of tomatoes.