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Ted's Toys makes toy airplanes, boats, and cars.  The materials used are plastic, wood...

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cbromm | Honors

Posted July 15, 2013 at 4:15 PM via web

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Ted's Toys makes toy airplanes, boats, and cars.  The materials used are plastic, wood strips, and steel.  Each airplane uses 150 grams of plastic, 25 inches of wood strips, and 100 grams of steel.  Each boat uses 75 grams of plastic, 150 inches of wood strips, and 20 grams of steel; and each car uses 100 grams of plastic and 150 grams of steel.  If Ted's has on hand 18,250 grams of plastic, 2750 inches of wood strips, and 20,200 grams of steel, how many planes, boats, and cars should be made to use up all these supplies?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 15, 2013 at 4:47 PM (Answer #1)

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Ted's Toys makes toy airplanes, boats, and cars.  The materials used are plastic, wood strips, and steel.  Each airplane uses 150 grams of plastic, 25 inches of wood strips, and 100 grams of steel.  Each boat uses 75 grams of plastic, 150 inches of wood strips, and 20 grams of steel; and each car uses 100 grams of plastic and 150 grams of steel.  Ted's has on hand 18,250 grams of plastic, 2750 inches of wood strips, and 20,200 grams of steel. Let the number of planes, boats, and cars to be made to use up all the supplies be a, b, c. This gives:

150a + 75b + 100c = 18250

25a + 150b = 2750

100a + 20b + 150c = 20200

Solving the three equations gives a = 50,b = 10 and c = 100.

Ted's Toys should make 50 planes, 10 boats and 100 cars to use up all their supplies.

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flbyrne | (Level 3) Assistant Educator

Posted July 15, 2013 at 4:54 PM (Answer #2)

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We have 3 equations and three variables:

(1) 150A+75B+100C=18250

(2) 25A+150B=2750

(3) 100A+20B+150C=20200

There are many ways you can solve this. Here is one:

From (2): A=110-6B

Substitute A into (1) and (3):

(4) 150(110-6B) + 75B +100C=18250

(5) 100(110-6B) + 20B +150C=20200

Multiply (4) by -1.5:

(6) -225(110-B) - 112.5B -150C = -27375

Add (6) to (5) to eliminate C:

-125(110-6B)-92.5B=-7175

Solving for B: B=10 boats

Replace B into (2): A=50 airplane

Solve (3) for C: C=(20200-(5000+200))/150=100 cars

Verify using (1):

150*50+75*10+100(100)=18250

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