Math word problem.?

The president of Speedy Airlines has discovered that her competitor, Zip Airlines, has purchased 13 new airplanes from Commuter Aviation for a total of $15.9 million. She knows that Commuter Aviation produces three types of planes and that type A sells for $1.1 million, type B sells for $1.2 million and type C sellls for $1.7 million. The president of Speedy Airlines also managed to find out that Zip Airlines purchased 5 more type A planes than type C planes. How many planes of each type did Zip Airlines purchase?

Math word problem.?
Let a be type A, etc


so your starting equations are


a+b+c = 13





1.1a+1.2b+1.7c=15.9





c = a-5


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substitute value for c


a+b+a-5=13


combine like terms


2a+b-5=13


add 5 to both sides %26amp; subtract 2a from both sides


b=18-2a


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1.1a+1.2b+1.7c=15.9


multiply both sides by 10


11a+12b+17c=159


substitute values for c %26amp; b


11a+12(18-2a)+17(a-5)=159


simplify


11a+216-24a+17a-85=159


simplify


4a+131=159


subtract 131 from both sides


4a=159-131


4a=28


divide both sides by 4


a= 7 ........................................... 7 type A planes


substitue values


b=18-2a=18-2(7)=18-14= 4 .. 4 type B planes


c=a-5=7-5= 2 ......................... 2 type C planes


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PROOF


a+b+c = 13


7+4+2 = 13


13=13





1.1a+1.2b+1.7c=15.9


1.1(7)+1.2(4)+1.7(2)=15.9


simplify


7.7+4.8+3.4=15.9


15.9=15.9

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