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Charlie is making costumes for a school show. One day he made 2 cloaks and 3 dresses. The total amount of material he used was 9·6 square metres. (a) Write down an equation to illustrate this information. 1 (b) The following day Charlie made 3 cloaks and 4 dresses. The total amount of material he used was 13·3 square metres. Write down an equation to illustrate this information. 1 (c) Calculate the amount of material required to make one cloak and the amount of material required to make one dress.

 Sep 18, 2019
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Let x be the square meters of material used to make 1 cloak  and y be the  square meters of material used to make 1 dress

 

We have these equations   :

 

2x  +  3y   =   9.6        multiply through by  -4   ⇒   -8x  - 12y  = -38.4        (1)    

3x  +  4y   = 13.3        multiply through by  3    ⇒    9x  + 12y  =  39.9        (2)

 

Add (1)  and (2)    and we get that

 

x  =  1.5  =  the square meters of material needed to make one cloak

 

And the number of square meters to make one dress can be found thusly :

 

2 (1.5) + 3(y)  = 9.6

 

3  + 3y  =  9.6              subtract 3 from both sides

 

3y   = 6.6                   divide both sides by  3

 

y  = 2.2  = the square meters of material needed to make one dress

 

cool cool cool

 Sep 18, 2019

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