Introduction to Algebraic Word Problems

Algebraic word problems are math problems expressed using words rather than just equations and numbers. They require translating the written words into mathematical equations in order to solve them.

In this article we will discuss how to solve the algebraic word problems.

Basic Approach

When starting an algebraic word problem, follow these basic steps:

• Read the entire problem carefully, more than once if necessary, to understand what the problem is asking.
• Identify the key information and quantities given in the problem. Make sure you understand what each quantity represents.
• Define variables to represent unknown values. Typically, a letter like x or y is used.
• Translate the wording into mathematical equations with your defined variables.
• Solve the equations to find the value of the unknowns.
• Answer the question asked in the problem using your solved values.

Types of Algebraic Word Problems

Some common types of algebraic word problems include:

Age problems

These involve determining a person’s age or the amount of time that has elapsed. Equations use variables representing ages and setups like “Tom’s age in 5 years” or “Mary is 2 years older than John.”

Mixture problems

These involve combining two amounts with different values per unit, like solutions mixed at varying concentrations. Equations have terms for the total amount, amounts of each mixture, and concentrations.

Geometry problems

These involve perimeter, area, angles, and other geometric operations. Equations relate the geometric values like the area of a rectangle in terms of its width and length.

Interest problems

These involve calculating interest earned based on principles like simple or compound interest over time. Equations relate interest amounts, rates, principal investments, and time periods.

Divisions and Fractions in Word Problems

Some tips when word problems involve divisions or fractions:

• Use a variable like x to represent a fractional amount or what is being divided.
• Make sure to keep track of the original total amount and what fractions have been taken away.
• For interest and mixture problems with changing amounts over time, isolate each time period with separate variables and equations.
• Multiply both sides of the equation by the denominator to eliminate any fractions in the equations to be solved.

Example Word Problem

Jack and Jill each set aside part of their weekly $10 allowance. Jack put 2/5 of his $10 into savings. Jill put 1/4 of her $10 into savings. How much more money did Jack put into savings than Jill?

Solution

Let x = Jack’s amount put into savings

Let y = Jill’s amount put into savings

Jack put 2/5 of $10 into savings. 2/5 of $10 is (2/5) * $10 = $4.

So, x = $4

Jill put 1/4 of $10 into savings. 1/4 of $10 is (1/4) * $10 = $2.50.

So, y = $2.50

Jack put x – y more into savings than Jill.

x – y = $4 – $2.50 = $1.50

Therefore, the amount Jack put into savings that was $1.50 more than Jill.

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