SOLUTION: An electronics company makes two types of switches. Type A takes 3 minutes to make and requires ​$2 worth of materials. Type B takes 4 minutes to make and requires ​$4 of mater

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An electronics company makes two types of switches. Type A takes 3 minutes to make and requires ​$2 worth of materials. Type B takes 4 minutes to make and requires ​$4 of mater      Log On


   

Question 1158749: An electronics company makes two types of switches. Type A takes 3 minutes to make and requires ​$2 worth of materials. Type B takes 4 minutes to make and requires ​$4 of materials. In the latest production​ batch, it took 27 hours to make these​ switches, and the materials cost ​$1400. How many of each type of switch were​ made?
Answer by ikleyn(52879) About Me  (Show Source):
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Let "a" be the number of the type A items, and let "b" be the number of the type B items.

Then from the condition, you have these two equations


    3a + 4b = 1620 minutes     (1)    (1620 = 27 hours * 60 minutes, the time spent)

    2a + 4b = 1400 dollars     (2)    (Cost of the material).


To solve the system of equations, from equation (2) subtract equation (1). You will get

    3a - 2a = 1620 - 1400,   or

     a      = 220.


Next, substitute the found valu of a= 220 into equation (2). You will get

    2*220 + 4b = 1400,

    4b = 1400 - 2*220 = 960

     b                = 960/4 = 240.


ANSWER.  220 items of the type A and 240 items of the type B.

Solved.