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Applications of Linear Systems

Applications of Linear Systems. Hyewon and Jinhan. Word Problem.

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Applications of Linear Systems

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  1. Applications of Linear Systems Hyewon and Jinhan

  2. Word Problem • Your car’s manual recommends that you use at least 89-octane gasoline. Your car’s 16-gallon gas tank is almost empty. How much regular gasoline (87-octane) do you need to mix with premium gasoline (92-octane) to produce 16 gallons of 89-octane gasoline?

  3. Solution • An octane rating is the percent of isooctane in the gasoline, so 16 gallons of 89-octane gasoline contains 89% of 16, or 14.24, gallons of isooctane. • Verbal Model Volume ofVolume of Volume of regular + premium = 89-octane Isooctane inIsooctane in Isooctane in regular + premium = 89-octane

  4. Labels Volume of regular = x Volume of premium = y Volume of 89-octane = 16 Isooctane in regular = 0.87x Isooctane in premium = 0.92y Isooctane in 89-octane = 14.24 • Algebraic Model x + y = 16 Equation 1 0.87x + 0.92y = 14.24 Equation 2

  5. Use substitution. Solve Equation 1 for y and substitution into Equation 2. y = 16 – xSolve Equation 1 for y. 0.87x + 0.92(16-x) = 14.24Substitution 16 – x for inEquation 2. -0.005x = -0.48Simplify x = 9.6Solve for x. 9.6 + y = 16Substitute 9.6 for x in Equation 2. y = 6.4Solve for y.

  6. Check • Substitute in each equation to check your result. Equation 1 x + y = 16 9.6 + 6.4 = 16 16 = 16 Equation 2 0.87x + 0.92y = 14.24 0.87x(9.6) + 0.92(6.4) = 14.24 8.352 + 5.888 = 14.24 14.24 = 14.24 • You need to mix 9.6 gallons of regular gasoline with 6.4 gallons of premium to get 16 gallons of 89-octane gasoline.

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