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Solving A System of Equations

Solving A System of Equations. Celeste S alinas & Tanya Garcia 12/19/13 5b. Problem Situation. The cost of a motorcycle is $200 less than one-third of the cost of a truck. Three motorcycles and a truck cost $35,400. Find the cost of a motorcycle. Define Variables.

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Solving A System of Equations

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  1. Solving A System of Equations Celeste Salinas & Tanya Garcia 12/19/13 5b

  2. Problem Situation • The cost of a motorcycle is $200 less than one-third of the cost of a truck. • Three motorcycles and a truck cost $35,400. • Find the cost of a motorcycle.

  3. Define Variables T = cost of one of the trucks M = cost of one of the motorcycles

  4. System of Equations • M = (1/3)T – 200 • 1T + 3M = 35,400

  5. Solution Method • We are going to solve this by substitution.

  6. Step 1 of Solution • T + 3(3T – 200) = 35400 Instead of M use 3T – 200 T + T – 600 = 35400 Use the distributive property 2T – 600 = 35400 Combine like terms + 600 = + 600 Add 600 to both sides 2T = 36000 Divide both sides by 2 2 = 2 T = 18000 ♥

  7. Step 2 of Solution M = (1/3)18000 – 200 Replace T with 1800 M = 6000 - 200 Multiply M = 5800 Subtract

  8. Solution to the System of Equations • (M, T) (5800,18000)

  9. Check of Solution • 5800=(1/3)18000-200 • 1(18000)+3(5800)=35400

  10. Solution in the Problem Situation • The cost of the motorcycle is $5,800. • The cost of the truck is $18,000.

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