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Simultaneous linear equations: VJC 2024 Promo Q1

Attempt the question on paper, then open the worked solution to check your method.

Victoria Junior College2024 PromoPromo Q1●○○ Foundational4 marks

What this question tests

Systems of linear equations.

Question

A small garment shop produces dresses, blouses and skirts. The production process includes cutting, sewing and packaging. The table below shows the time in minutes required to produce each piece of garment. The total time spent on cutting, sewing and packaging are 3150, 4300 and 480 minutes per week respectively.

Garment	Time required (min)
Garment	Cutting	Sewing	Packaging
Dress	45	70	8
Blouse	50	60	6
Skirt	20	25	3

Write down and solve equations to find the number of pieces of each garment the shop produces each week. [4]

Show full worked solution▾

Let $x$ , $y$ and $z$ be the number of dresses, blouses and skirts produced per week respectively.

$45x+50y+20z=3150$

$70x+60y+25z=4300$

$8x+6y+3z=480$

By GC, $x=30$ , $y=20$ , $z=40$ .

The shop produces 30 dresses, 20 blouses and 40 skirts each week.

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