Problem 74 - Algebra and Trigonometry

Question

One of the best ways to learn how to solve a word problem in algebra is to design word problems of your own. Creating a word problem makes you very aware of precisely how much information is needed to solve the problem. You must also focus on the best way to present information to a reader and on how much information to give. As you write your problem, you gain skills that will help you solve problems created by others. The group should design five different word problems that can be solved using linear equations. All of the problems should be on different topics. For example, the group should not have more than one problem on simple interest. The group should turn in both the problems and their algebraic solutions.

Step-by-Step Solution

Answer

The exercise is successfully completed by coming up with five different word problems involving linear equations. These problems are based on Speed & Distance, Proportions, Cost Calculation, Simple Interest, and Temperature Conversion. The corresponding equations are \(d = 60 \times 5\), \(4/8 = x/16\), \(c = 10 \times 20\), \(I = 500 \times (5/100) \times 3\), and \(C = (F - 32)(5/9)\) respectively.

Step 1: Problem 1: Speed & Distance

A car travels at a speed of \(60\) km/h for \(5\) hours. Write the equation to find the distance covered by the car?

Step 2: Solution 1

Using speed is equal to distance over time, the equation is \(d = 60 \times 5\), where \(d\) is the distance covered.

Step 3: Problem 2: Proportions

A recipe for a cake requires \(4\) cups of flour to make \(8\) servings. Write the equation to find out how much flour is needed for \(16\) servings?

Step 4: Solution 2

The equation can be given as \(4/8 = x/16\), where \(x\) is the cups of flour required for \(16\) servings.

Step 5: Problem 3: Cost Calculation

A retailer sells a product for \(10\) dollars each. Write the equation to calculate how much will \(20\) products cost?

Step 6: Solution 3

The equation is given by \(c = 10 \times 20\), where \(c\) is the cost of \(20\) products.

Step 7: Problem 4: Simple Interest

A man invested \(500\) dollars at an annual interest rate of \(5\%\). Write down the equation for the simple interest earned after \(3\) years.

Step 8: Solution 4

The formula for simple interest is \(I=PRT\), where \(P\) is principal, \(R\) the rate of interest, and \(T\) the time. So the equation becomes \(I = 500 \times (5/100) \times 3\), where \(I\) is the interest.

Step 9: Problem 5: Temperature Conversion

Write the linear equation to convert temperature in Fahrenheit to Celsius. The formula is \(C = (F - 32)(5/9)\), where \(C\) is Celsius and \(F\) is Fahrenheit.

Step 10: Solution 5

The equation \(C = (F - 32)(5/9)\) is the linear equation to convert Fahrenheit to Celsius.