Question

A shipping company charges a flat rate of $7 for packages weighing five pounds or less, $15 for packages weighing more than five pounds but less than ten pounds, and $22 for packages weighing more than ten pounds. During one hour, the company had 13 packages that totaled $168. The number of packages weighing five pounds or less was three more than those weighing more than ten pounds. The system of equations below represents the situation.

Answer 1

To solve the problem, let x be the number of packages weighing more than ten pounds. Then, the number of packages weighing five pounds or less is x + 3. Setting up the equation based on the total cost of the packages, we find that x = 3. Therefore, there are 3 packages weighing more than ten pounds and 6 packages weighing five pounds or less.

Step-by-step explanation:

To solve this problem, let's define some variables. Let x be the number of packages weighing more than ten pounds. Therefore, the number of packages weighing five pounds or less will be x + 3.

Now, we can set up the equation based on the total cost of the packages: 7(x + 3) + 15(13 - x - (x + 3)) + 22x = 168.

Simplifying the equation, we get 7x + 21 + 15(13 - 2x - 3) + 22x = 168.

Expanding and simplifying further, we have 7x + 21 + 195 - 30x - 45 + 22x = 168. Combining like terms, we get -x + 171 = 168.

Lastly, we can solve for x by subtracting 171 from both sides: -x = -3. Therefore, x = 3.

The number of packages weighing more than ten pounds is 3, and the number of packages weighing five pounds or less is 6.