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.
+128406 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
