https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/dogs-cats-and-bears-in-a-pet-store-visual-argument 2021-06-29T20:27:57Z Analyzing structure word problem: pet store (1 of 2) Sal solves a word problem about the unknown number of bears, cats, and dogs in a pet store. This is part 1 where Sal uses a visual reasoning. Sal Khan video https://cdn.kastatic.org/googleusercontent/p29Zi4lkiwDk4KH1X9Ud__RtCwTROhtBbzi7FKVeExTrX6HH03QXkMs1OtyoMdYkTZElpSgxv5WSsrzNqJf-iX4 Analyzing structure word problem: pet store (1 of 2) Sal solves a word problem about the unknown number of bears, cats, and dogs in a pet store. This is part 1 where Sal uses a visual reasoning. https://cdn.kastatic.org/ka-youtube-converted/glEP04Pzap8.mp4/glEP04Pzap8.mp4 354 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/dogs-cats-and-bears-in-a-pet-store-analytic-argument 2021-06-29T20:28:00Z Analyzing structure word problem: pet store (2 of 2) Sal solves a word problem about the unknown number of bears, cats, and dogs in a pet store. This is part 2 where Sal uses an algebraic reasoning. Sal Khan video https://cdn.kastatic.org/googleusercontent/oc72cMPu1pdHl-SharIwDzKCJTLSclRLmLLP69wI7q1HSqwVy03Sr0ZXnbkfgZa62Vicg4ncLMUFcQVRkefkSK-hwQ Analyzing structure word problem: pet store (2 of 2) Sal solves a word problem about the unknown number of bears, cats, and dogs in a pet store. This is part 2 where Sal uses an algebraic reasoning. https://cdn.kastatic.org/ka-youtube-converted/mpHMuaVW0DI.mp4/mpHMuaVW0DI.mp4 164 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/combining-mixtures-example 2021-11-29T20:55:31.597838339Z Combining mixtures example Figure out how much of two gasoline mixtures to combine to get gasoline with a certain concentration of ethanol. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Combining mixtures example Figure out how much of two gasoline mixtures to combine to get gasoline with a certain concentration of ethanol. https://cdn.kastatic.org/ka-youtube-converted/xMADEddxSEo.mp4/xMADEddxSEo.mp4 348 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/applying-rational-equations-1 2021-06-29T20:27:56Z Rational equations word problem: combined rates Sal solves a word problem about the combined leaf-bagging rates of Ian and Kyandre, by creating a rational equation that models the situation. Sal Khan video https://cdn.kastatic.org/googleusercontent/YtleC_3qgEHL0HU_I_NrYrzg4VexqBWMUriZuKQhM9obdO5eCwtQgWpcnFi6tvnvewboLuMb2WDIyLssHu-ThMon Rational equations word problem: combined rates Sal solves a word problem about the combined leaf-bagging rates of Ian and Kyandre, by creating a rational equation that models the situation. https://cdn.kastatic.org/ka-youtube-converted/gD7A1LA4jO8.mp4/gD7A1LA4jO8.mp4 326 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/applying-rational-equations-2 2021-06-29T20:27:54Z Rational equations word problem: combined rates (example 2) Sal solves a word problem about the combined deck-staining rates of Anya and Bill, by creating a rational equation that models the situation. Sal Khan video https://cdn.kastatic.org/googleusercontent/xd7Jt9VaRGLK_25RZC_OckJ3IwnIUcB47YC831p09S0kuqAMQGT52kp58nWiJeLtfUdpisjBuqRrTcLi_rU2qE3e Rational equations word problem: combined rates (example 2) Sal solves a word problem about the combined deck-staining rates of Anya and Bill, by creating a rational equation that models the situation. https://cdn.kastatic.org/ka-youtube-converted/E1j8W64NQ0Y.mp4/E1j8W64NQ0Y.mp4 360 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/e/mixtures-and-combined-rates-word-problems 2024-08-12T05:01:46.814165037Z Mixtures and combined rates word problems Determine individual rates and overall outcomes from real world contexts involving combinations of different speeds or concentrations. Charlotte Auen exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/applying-rational-equations-3 2021-06-29T20:27:58Z Rational equations word problem: eliminating solutions Sal solves a word problem about the combined pool-filling rates of two water hoses, by creating a rational equation that models the situation. The equation has a solution that is eliminated due to the context. Sal Khan video https://cdn.kastatic.org/googleusercontent/9cXY1GgvhNKJRdWPqqvy_FI0k9arbfjCEgX_yOawi2dZ1UgOKJqKZdcjR6v9-OhbaxA8zkBdbRE496qqUiUTMiUY Rational equations word problem: eliminating solutions Sal solves a word problem about the combined pool-filling rates of two water hoses, by creating a rational equation that models the situation. The equation has a solution that is eliminated due to the context. https://cdn.kastatic.org/ka-youtube-converted/B0Z4s38YIgQ.mp4/B0Z4s38YIgQ.mp4 479 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/reasoning-through-inequality-expressions 2021-06-29T20:27:49Z Reasoning about unknown variables Sal solves the following challenge: Given that a>0, b<0, and a/b>a*b, what further can we learn about the variables? Sal Khan video https://cdn.kastatic.org/googleusercontent/ICFNg5rJ8ZvP2e6NXy6oRZKZZdpLI9F9gJqCL-Ud7Qy1G7YSbgGjTebKUET-F7PEXcq0T-n50ueGcoXPi22FE_E5 Reasoning about unknown variables Sal solves the following challenge: Given that a>0, b<0, and a/b>a*b, what further can we learn about the variables? https://cdn.kastatic.org/ka-youtube-converted/0_VaUYoNV7Y.mp4/0_VaUYoNV7Y.mp4 367 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/using-expressions-to-understand-relationships 2021-06-29T20:27:53Z Reasoning about unknown variables: divisibility Sal solves the following challenge: Given the positive integers a, b, and c, where a is a multiple of c and (a+b)/c is an integer. Is b necessarily a multiple of c? Sal Khan video https://cdn.kastatic.org/googleusercontent/cGBRRu53qLFt_utBDjDWneRGmtF6LWFGp_SKyzgbKVvsS1WsxITkq6Xyi9qbukLtItOJI0Dw9bEX37Dxc-BoeQk Reasoning about unknown variables: divisibility Sal solves the following challenge: Given the positive integers a, b, and c, where a is a multiple of c and (a+b)/c is an integer. Is b necessarily a multiple of c? https://cdn.kastatic.org/ka-youtube-converted/zTLxxezKUT8.mp4/zTLxxezKUT8.mp4 218 Modeling with rational functions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/structure-in-rational-expression 2021-07-03T00:17:01Z Structure in rational expression Analyzing an elaborate rational expression to determine what's bigger: the value of that expression at some unknown c, or the number of times the expression is equal to 0? This is algebraic reasoning at its best! Sal Khan video https://cdn.kastatic.org/googleusercontent/_Xc1E5xBoC2wbcXTvRm_ApyvEM6D33g0ZwJzN7foP52tKb2t9OFcQRd3dqvPdOJQCMYro7VFMVZKKM2uDQ9ZutT2EQ Structure in rational expression Analyzing an elaborate rational expression to determine what's bigger: the value of that expression at some unknown c, or the number of times the expression is equal to 0? This is algebraic reasoning at its best! https://cdn.kastatic.org/ka-youtube-converted/mNgW6SAQLhk.mp4/mNgW6SAQLhk.mp4 281 Modeling with rational functions