# Solving Word Problems In Algebra

If the boiling point of water is and the melting point of water is , find the linear functions that convert from one scale to the other.This problem asks us to find a conversion function that takes a Fahrenheit temperature reading and turns it into a Celsius temperature reading.

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The main difficulty is translation of the details of the word problem into the kinds of mathematical expressions that you have learned to handle. This step may seem obvious, but you will save yourself much time and difficulty if you take some time to carefully read what the problem says. A word problem may provide you with enough details to calculate all sorts of parameters, but the problem probably will only be asking for one or two. You don't need to be an artist to do this-just draw something that you can understand and that helps you organize your thoughts about the problem. The mathematical expressions that you glean from the word problem will involve an unknown value (or values) at some point (one of which may be the result from step 2 above); try to identify what this value is and assign it a variable symbol. Problems from the real world involve units, and you need to keep track of them. If you have carefully performed the preceding steps, you should be in good shape to write the correct expressions. The result should be a solution that fulfills the requirement you wrote down in step 2 (that is, whatever the problem is asking for). Does the problem ask for a speed but you've ended up with units of acceleration in your answer?

Here are some steps that will help you organize the process of translating from words to mathematical expressions that you can solve. You may not be able to visualize all the details, but you should gain a mental picture of what is generally being discussed. Thus, figure out what you are trying to find and write it down. If the problem involves a moving automobile, for instance, you don't need to draw a professional rendition when a box or something similar (even marked "car" if necessary) will do. Write down this assignment for reference as you solve the problem (for instance, " = the velocity of the car"). You've probably gone astray somewhere along the line.

This problem illustrates the process of unit conversion; a year is the same as 525,600 minutes even though 1 ≠ 525,600.

Bill takes a trip in which he drives a third of the time at 30 miles per hour, a third of the time at 50 miles per hour, and a third of the time at 70 miles per hour.

So his normal pay of 40 × \$12 = \$480, plus his overtime pay of 12 × \$15 = \$180 gives us a total of \$660 There are 12 girls!

And 3b = 4g, so b = 4g/3 = 4 × 12 / 3 = 16, so there are 16 boys So there are now 12 girls and 16 boys in the class, making 28 students altogether.We know that we can find the distance traveled by multiplying the speed and the time traveled at that speed (for instance, if we travel 2 hours at 30 miles per hour, we have gone 60 miles).In addition, we know that Bill travels a third of the time ( The Celsius (C) and Fahrenheit (F) temperature scales are related by a linear function. Well, it's going to be w plus w plus 2w plus 2w. The perimeter of this garden is going to be equal to w plus 2w plus w plus 2w, which is equal to what? But they also tell us that the actual numerical value of the perimeter is 60 feet. So this perimeter 6w must be equal to 60 if we assume that we're dealing with feet. We can divide both sides of this equation by 6 so that we have just a w on the left-hand side. So let's draw this garden here, Tina's garden. So if this is the width, then this is also going to be the width. And they tell us that the length of the garden is twice the width. You may be surprised at how far you can get by approaching the problem systematically.First, let's identify what the problem is asking for: a total trip time, which we can call , which is the value we want to calculate.Check −14: −14(−14 2) = (−14)×(−12) = 168 YES Check 12: 12(12 2) = 12×14 = 168 YES So there are two solutions: -14 and -12 is one, 12 and 14 is the other.Note: we could have also tried "guess and check": And so L = 8 or −14 There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

## Comments Solving Word Problems In Algebra

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