# Algebra Word Problem - practice problems

• enggM
In summary, the problem asks for the original fraction, which is 1.5. When multiplied by 3, it becomes equivalent to 1. When increased by 3, it becomes equivalent to 2.
enggM

## Homework Statement

The problem goes like this: The sum of 2 numbers is 25. If 2/3 of the smaller one is 2 more than 1/4 of the larger one, find the 2 numbers.

Any hints on how to start off this one? What should I let x= be?

When i attempted to solve this i let 2/3x = the smaller number and then the other number is 1/4(2/3x+2) well that's how i understood this problem and after that the solution looked really bad, i got really large fractions as an answer.

Last edited:
Let ##x## be the smaller number and ##y## be the larger number. Can you now try to frame some equations?

ahh thank you very much well i'll try it.

enggM said:

When i attempted to solve this i let 2/3x = the smaller number and then the other number is 1/4(2/3x+2) well that's how i understood this problem and after that the solution looked really bad, i got really large fractions as an answer.
The problem said 2/3 of the smaller number. Setting "2/3x = the smaller number" says that the smaller number IS 2/3 of some other number. You have it backwards.

so basically i might have switched the two numbers is that what you're implying? ohhh i see got to try it :)

enggM said:
so basically i might have switched the two numbers is that what you're implying? ohhh i see got to try it :)
Seems to me you reversed all three operations, the 2/3, the +2, and the 1/4.

oh thanks for all of your hints i finally solve it. i forgot the role of 25 there so the setting was let x = smaller then 25-x = the larger then set up the equation which is 2/3(x)=1/4(25-x)+2. Now to the next one :) 2]The denominator of a fraction exceeds its numerator by 5. If the numerator is multiplied by 3, and the denominator is increased by 3, the resulting fraction is equivalent to 1. Find the original fraction. ill be back tomorrow to cook up the constraints and equations any hints would be appreciated though :)

enggM said:
Now to the next one :) 2]The denominator of a fraction exceeds its numerator by 5. If the numerator is multiplied by 3, and the denominator is increased by 3, the resulting fraction is equivalent to 1. Find the original fraction. ill be back tomorrow to cook up the constraints and equations any hints would be appreciated though :)
Since this is a new question, please start a new thread. Be sure to use the homework template.

## 1. What are some common keywords to look for in algebra word problems?

Some common keywords to look for in algebra word problems are "sum," "difference," "product," "quotient," "per," "more than," "less than," "equal to," "ratio," "percentage," and "of."

## 2. How should I approach solving an algebra word problem?

The first step in solving an algebra word problem is to carefully read and understand the problem. Then, define the variables and create an equation to represent the problem. Finally, solve the equation and check your answer to make sure it makes sense in the context of the problem.

## 3. What is the order of operations in algebra?

The order of operations in algebra is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This means that parentheses should be simplified first, followed by exponents, then multiplication and division, and finally addition and subtraction.

## 4. How do I know if I need to use a variable in an algebra word problem?

Variables are used in algebra to represent unknown quantities. If the problem asks for a value that is not given, you will need to use a variable to represent it. Additionally, if there is a relationship between two or more quantities in the problem, a variable may be needed to represent that relationship.

## 5. Are there any tips for checking my answer to an algebra word problem?

One helpful tip for checking your answer to an algebra word problem is to plug it back into the original equation and see if it makes the equation true. You can also check your answer by using estimation or by solving the problem in a different way to see if you get the same result.

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