Problem 41 - Basic College Mathematics

Question

An electrical supplier sells rolls of SJO 14-3 cable to a company that makes extension cords. It takes \(\frac{7}{3} \mathrm{ft}\) of cable to make each cord. How many extension cords can be made with a roll of cable containing \(2240 \mathrm{ft}\) of cable?

Step-by-Step Solution

Answer

960 cords.

Step 1 - Identify the total length of the cable roll

The total length of the cable available is given. In this case, it is \(2240 \mathrm{ft}\).

Step 2 - Determine the length of cable needed for each extension cord

The length of cable required to make one extension cord is given as \(\frac{7}{3} \mathrm{ft}\).

Step 3 - Calculate the number of extension cords that can be made

To find the number of extension cords that can be made, divide the total length of the cable roll by the length of cable needed for one extension cord: \ \[\text{Number of cords} = \frac{2240 \mathrm{ft}}{\frac{7}{3} \mathrm{ft}} = 2240 \times \frac{3}{7} = 2240 \times \frac{3}{7} = 960 \text{cords}\.\]

Key Concepts

mathematical problem solving

Mathematical problem solving revolves around understanding and solving problems using mathematical concepts and techniques. Breaking down a word problem into simpler steps can make it easier to approach and solve. Here, the problem asks how many extension cords can be made from a given length of cable. You'll start by identifying the given information: the total length of the cable and the amount needed for each cord. By systematically working through each piece of information and performing the necessary calculations, you can find the solution. Always read the problem carefully, identify what is being asked, and note down the relevant data.

division of fractions

Division of fractions is a crucial skill in problem-solving, especially for word problems involving measurements. In this exercise, we need to divide a whole number by a fraction to find out how many extension cords can be made. Here’s how: When dividing by a fraction, multiply by its reciprocal. For example, dividing 2240 feet of cable by \(\frac{7}{3}\) feet per cord, we should compute: \[ \frac{2240 \text{ ft}}{\frac{7}{3} \text{ ft}} = 2240 \text{ ft} \times \frac{3}{7} \] This multiplication thus simplifies to: \[ 2240 \times \frac{3}{7} = 2240 \times 0.42857 = 960 \text{ cords} \] Therefore, 960 extension cords can be made from the 2240 feet of cable. Remember, multiplying by the reciprocal turns the division into a multiplication problem, making it simpler to solve.

unit conversion in mathematics

Unit conversion is the process of converting a quantity from one unit to another. While this problem doesn’t explicitly involve converting units like miles to kilometers, understanding the concept can still be helpful. Breaking down units and ensuring consistency is vital. All measurements should be in the same unit before starting calculations. If units don't match, they must be converted appropriately. For instance, if the cable length was provided in meters instead of feet, it would need to be converted to feet first to match the per cord requirement. Consistent units ensure accurate calculations and understanding of the problem.