This makes sense, since consecutive means “in a row” and we’re always adding Solution: Let’s first define a variable, and use another table like we did before.Let \(J=\) the number of pounds of jelly candy that is used in the mixture. Let’s put this in a chart again – it’s not too bad.We can just put a negative sign in front of the variable.
Here’s an example of a Quadratic Inequality word problem.
We’ll also use inequalities a lot in the Introduction to Linear Programming section.
Then \(10-J\) equals the number of pounds of the chocolate candy. This one is a little more difficult since we have to multiply across for the Total row, too, since we want a Don’t worry if you don’t totally get these; as you do more, they’ll get easier.
We’ll do more of these when we get to the Systems of Linear Equations and Word Problems topics.
Now we have 6 test grades that will count towards our semester grade: 4 regular tests and 2 test grades that will be what you get on the final (since it counts twice, we need to add it HINT: For any problem with weighted averages, you can multiply each value by the weight in the numerator, and then divide by the sum of all the weights that you’ve used.
For example, if you had test 1 (say, an of your grade, you will take the weighted average as in the formula below.The problem is asking for both the numbers, so we can make “\(n\)” the smaller number, and “\(18-n\)” the larger.\(\begin2n-3\,\,\,=\,\,18-n\\underline\3n\,-3\,\,=\,\,\,18\\underline\\,\,3n\,\,\,\,\,\,\,\,\,\,=\,\,\,21\\,\frac\,\,\,\,\,\,\,\,\,\,\,=\,\,\frac\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,n=7\,\,\,\,\,\,\text\\,\,\,18-7=11\,\,\,\,\text\end\) Solution: We always have to define a variable, and we can look at what they are asking.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.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.We will see later that this is like a Slope that we’ll learn about in the Coordinate System and Graphing Lines including Inequalities section.Here’s the math: To get the rate of minutes to photos, we can set up a proportion with the minutes on the top and the photos on the bottom, and then cross multiply.To do this, let \(x=\) the repeating fraction, and then we’ll figure out ways to multiply \(x\) by ) just to the right of the decimal point; we get \(10x=4.\underline2525…\).Now we have to line up and subtract the two equations on the left and solve for \(x\); we get \(\displaystyle x=\frac\). Let’s see if it works: Put \(\displaystyle \frac\) in your graphing calculator, and then hit Enter; you should something like \)),“is no more than” (\(\le \)), “is at least” (\(\ge \)), and “is at most” (\(\le \)).