What Are the Possible Values of the Larger Number in This Inequality Problem?

In summary, the product of two numbers must be less than 340, and one number is 3 less than the other. To find the possible values of the larger number, we can use the equation x(x-3) < 340 and solve for x. By using test numbers, we can determine the interval of (-17, 20) as the solution set for x (the larger number). To find the smaller number, we can express x=y+3 and solve for y, or simply subtract 3 from each element in the solution set for x, resulting in the solution set for y as (-20, 17).
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Homework Statement


The product of two numbers is less than 340. One of the numbers is 3 less than the other. What are the possible values of the larger number?

Homework Equations


The Attempt at a Solution


Hope this is right...

xy < 340
then, because y=x-3
x(x-3) < 340
x^2 -3x -340 < 0
(x+17)(x-20) < 0

Then, by using test numbers I got the interval (-17 , 20) as my solution set.

Now, to get the larger number, do I just add 3 to every number in my possible values for y?
Since, x=y+3 ?

Then, possible values for x (larger number) will be (-15, 23) ?
Or, is what I'm doing wrong
Edit:Okay, by simple checking, 20 x 23 is larger than 340. So I guess I can't just add 3 to every y value I have. So, how do I do it? :)
Edit:I just realized again. Since my inequality is expressed in x (larger number) doesn't that mean I got the solution set for the larger number(which is asked by problem) already?? Please correct me if I'm wrong.
EDIT 3:So sorry for the much edits, but. In order to get the y value (I'm now asking for the smaller number), do I just minus 3 to every element in my solution set, since y is defined to be x-3 ? So, solution set for y= (-20, 17)?? Again, please correct me if I'm wrong.
/HELP!
 
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  • #2
Yes, you are correct. Another way to find the 'smallest' numbers is to express x=y+3 and solve y(y+3)<340 to find the solution set.
 

FAQ: What Are the Possible Values of the Larger Number in This Inequality Problem?

What are inequalities word problems?

Inequalities word problems are mathematical problems that involve comparing two quantities using inequality symbols, such as <, >, ≤, or ≥. These problems require solving for the unknown variable by determining which values make the inequality true.

How do I set up an inequality word problem?

To set up an inequality word problem, you must first identify the unknown variable and then use words or phrases to create an inequality statement. For example, "The number of apples is less than twice the number of oranges" can be written as a ≤ 2o, where a represents the number of apples and o represents the number of oranges.

What strategies can I use to solve inequalities word problems?

Some strategies for solving inequalities word problems include using algebraic techniques, graphing the inequality on a number line, and using trial and error with different values to see which make the inequality true.

Are there any common mistakes to avoid when solving inequalities word problems?

Yes, some common mistakes to avoid include switching the direction of the inequality symbol when multiplying or dividing by a negative number, forgetting to include the word "or" when writing the inequality statement, and not checking the solution to make sure it satisfies the original word problem.

How can I apply inequalities word problems in real life?

Inequalities word problems can be used in real life situations to represent relationships between quantities, such as income and expenses, weight and height, or speed and distance. These problems can help make decisions about budgeting, diet and exercise, or travel planning.

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