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Proportions - Problem 3
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
To solve a word problem using proportion, start by writing out the known ratio in words with the corresponding values. Next, set it equal to another fraction using the remaining information from the word problem and a variable for the unknown value. Solve using the technique most appropriate for the proportion (e.g., cross-multiplication, solving technique, etc...). Don't forget to check your answer by substituting the value of the variable into the original proportion.
One thing I hope you guys are learning by now is that Math really does show up in the real world. Ratios are really effective not only in shopping like this problem we're about to do but a lot of people use ratios in cooking. That's what you do if the recipe says it serves six people but you only want to serve four, you would use a ratio to change the ingredients. Similar idea here, the ratio of the sale price of a shirt to the original price is 2:3. If the original price is $18, what's the sale price?
Okay before we do this problem, I'm going to think about what I know about the real world. Sale means it's cheaper, right? So I'm hoping if I do all this Math correctly, I should get a number that's less than 18. If I get something that's bigger than 18, I knew I blew it.
Okay so the ratio of the sale price to a shirt to the original price is 2:3. I'm going to write it out using words so I can remember, sale/original is equal to 2/3, that's how I'm going to start with this problem. Then I'm going to write another ratio or another fraction using 18. 18 represents the original price so that's going to go in the bottom of my fraction, and I want to find out what's the sale. This is the proportion that I want to solve, sale price, sale price on top of original price, original price.
So from here you can cross multiply, you can use solving techniques or you can do lots of different ways like in terms of looking at what the multiplying ratio from one fraction to another is. It's totally up to you. I'm going to use solving techniques because I see that x divided by 18 is easy to undo by multiplying both sides by 18. If I multiply both sides by 18/1 then I'll have 2 times 18 is 36, over 3 is equal to x, and when I reduce that I can see that x is equal to 12.
Please make sure you put a dollar sign there so you remember that 12 represents the price of the shirt on sale. And that makes sense because the original price was 18, the sale is less than that and 2:3 is an equal fraction to 12/18. So ratios are something you might want to keep at the back of your brain for when you're out in the community going about your daily life because you can solve problems like this, be a real Math nerd and get the, you know figure out what your sale price would be.
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Sample Problems (8)
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The ratio of the sale price of a shirt to the original price is 2:3. If the original price is $18, what's the sale price?
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