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This Lesson (% Problems and Ratios) was created by by Nate(3500)
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~~~~Ratios~~~~ A ratio is represented by the following: (a.) 1 : 2 (b.) 1/2 (c.) 1 to 2 This tells us for every one of something there are two of something else. Let us do an example. You have have 3 : 4 ratio of dimes to quarters respectively. For every 3 dimes you have, you have 4 quarters. Say you had 6 dimes. You would have 8 quarters. 6/8 = 3/4 = 3 : 4 Now, let us do a problem: A triangle has a perimeter of 36 meters and a ratio of the sides as 2:3:4 .... what lengths are the sides? 2x : 3x : 4x 2x + 3x + 4x = perimeter = 36 9x = 36 x = 4 8 meters, 12 meters, and 16 meters Now, lets check how far you have gotten: You have a ratio of 3 : 2 of rubies to sapphires, and you have a ratio of 4 : 6 of sapphires to emeralds. In all you have 24 gems. How many of each do you have? Define using the variable "x": Rubies = 3x Sapphires = 2x Now, the number of sapphires (2x) can not be (4x) at the same time .... so we need to change 4 to two (4/2) : (6/2) 2 : 3 Emeralds = 3x 3x + 2x + 3x = 24 8x = 24 x = 3 Rubies: 9 Sapphires: 6 Emeralds: 9 ~~~~% Problems~~~~ A tank of gas may have, for example, 82% gasoline in it. That means that the AVERAGE of the liquids mixed together with who knows what percentages equal out to 82%. Lets start with an equation: Now, let us do a problem: If 2000 gallons of gas has a percentage of 92% gasoline, how many gallons of PURE gasoline will I need to add to get a 98% solution? Pure Gasoline is 100% gasoline in respect with (2000(92%) + x(100%))/(2000 + x) = 98% -120 = -0.02x 6000 = x 6000 gallons of 100% gasoline needs to be added .... Now, let us see if you could ever get 100% ? (2000(92%) + x(100%))/(2000 + x) = 100% 1840 + x = 2000 + x 0 = 160 Nope .... Now, how much of 93% gasoline solution would you need to extract to get a solution of 88% .. This lesson has been accessed 9669 times. |
