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However, word problems can present a real challenge if you don't know how to break them down and find the numbers underneath the story.
The answer key at the end of the post has detailed explanations to help you see the relationship between words and math in these types of questions. The sum of three consecutive positive integers is 111. Which equation shows how you could solve the problem? The term “consecutive positive integers” essentially means three whole numbers in a row, such as 1, 2, and 3. Since the numbers are consecutive, the second number in the series will be 1 more than x, and the third number in the series will be 2 more than x, so the three consecutive integers are x, x 1, and x 2.
The sum of these three terms needs to be 111, so your equation will be: (x) (x 1) (x 2)=111 You can simplify the expression by combining like terms—in this example, adding the variables and then adding the constants.
Now let’s do some problems that use some of the translations above.
We’ll get to more difficult algebra word problems later. Solution: We always have to define a variable, and we can look at what they are asking.
(x) (x 1) (x 2)=111 3x 1 2=111 3x 3=111 If you wanted to solve for x, you would isolate the variable by subtracting 3 from both sides, then dividing by 3: 3x 3=111 3x=108 x=36 So, the 3 consecutive integers are 36, 37, and 38. A This problem involves translating the words into mathematical expressions.
The first equation is quite simple to set up, since you know that she works 5 hours each week: x y=5 Use the information about the money Audrey earns to set up the second equation.Now, you can use this information to solve for x using the first equation: x y=5 x 2=5 x=3 So, she tutors for 3 hours each week. C Your first step is to find out how many grams of flour Oliver uses. Fill out the table as you parse each piece of information in the problem.He uses 340 grams per batch of biscuits, and he makes three batches. So, the amount of money she makes from rings is given by the expression 10(2x). You know that in total she made 5 at the craft fair.Things get a little more complicated in algebra when it comes to word problems, however.Sometimes, you’ll be given a word problem that requires you to WRITE the equation first and THEN solve it. C) She tutors for 2 hours and babysits for 3 hours. She sells necklaces for , bracelets for , and rings for . How many necklaces, bracelets, and rings did Iris sell?Some algebra problems on the GED Mathematical Reasoning test are straightforward: Solve a given equation for x.Once you know the basic rules for solving, these are pretty simple.Note that Using Systems to Solve Algebra Word Problems can be found here in the Systems of Linear Equations and Word Problems section.Now that you can do these difficult algebra problems, you can trick your friends by doing some fancy word problems; these are a lot of fun.The problem is asking for a number, so let’s make that \(n\).Now let’s try to translate word-for-word, and remember that the “opposite” of a number just means to make it negative if it’s positive or positive if it’s negative.