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Course: Pre-algebra>Unit 14

Lesson 4: Constructing linear models for real-world relationships

Modeling with linear equations: gym membership & lemonade

Constructing linear equations to solve word problems. Created by Sal Khan.

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• at Sal mentions break even
what does that mean?
• Break even is the point when revenue equals expenses and so there is no profit or loss incurred.
If the expense amounts to \$25 then the break even point is when revenue is \$25 also. At this point there will be no loss or profit as 25-25 = 0
• What is the meaning of break even in the problem??
• Break even means when the cost or expenses are equal to the revenue earned. That is there is 0 profit or loss incurred.
Here Bobby and Petra's expense will be \$25 so if they also earn a revenue of \$25 they will break even.
• In the lemonade stand example doesnt -needing to make \$25 to break even (ie to have 0)- mean that the y intercept is -25?
• Sal defined y as the revenue (although he worded it ambiguously), meaning the amount of money that goes into their register. Thus he got the equation y=0.45x. Because revenue must equal cost to break even he plugged 25 in for y.

If y had been defined as profit (how much better off are you than before you started the business, or Revenue - Cost) then the y-intercept would indeed be -25 and the equation would be y=0.45-25. In this case you would be looking for where profit is zero and would plug 0 in for y, resulting in the same answer of 56 cups of lemonade must be sold to break even.
• help me!1!!ferdie's car uses 15 liters of gasoline to travel 200 kilometers. At that rate, how much gasoline will his car use to travel 300 kilometers
• ferdie's car will use 22.5 liters after 300 kilometers
• help not looking for answer but help on variable and equation
A one-cup serving of orange juie contains 3mg les than four times the amount of vitamin C as a one-cup serving of pineapple juice. Servings of the 2 juices contain a total of 122 mg of vitamin C. How many milligrams of vitamin C are in a serving of each type of juice?
• Which equations can you write from the information given?
Starting with the easier one, servings of the 2 juices, I get that o + p = 122. Or, orange juice + pineapple juice = 122mg of vitamin C. I just chose o = orange juice and p = pineapple juice. You can pick any variable you like, as long as you can keep them straight and you are consistent.

Now the tricky one, or confusing one. Orange juice contains 3mg less than 4 times a serving of pineapple juice. When I learned how to do these I found it really helped to substitute an = for certain words in the text. So, I would cross out words like "contains, equals, has" and such then it became easier to see which parts of the word problem were on which side of the equation. So, I get that o = 4p - 3, from that statement.
Now we have 2 equations for 2 variables and should be able to solve for each. Does that help?
• At isn't 9 times 4 = 36, not 35? :)
• Yes, many people have been commenting about it. It was just a simple mistake though. :)
• The way the question is worded makes it very confusing.
"At the end of the year" should really be replaced with "after a year"
• is there a shortcut of doing this?