Simultaneous linear equations: YIJC 2024 Promo Q1

Yishun Innova Junior College2024 PromoPromo Q1●○○ Foundational4 marks

What this question tests

Systems of linear equations.

Question

A concert sells tickets under three different age categories: ‘Senior Citizen’, ‘Adult’ and ‘Child’. Three groups of people A, B and C went to the concert on 3 different days. For Group A, all tickets were purchased at the original prices. For Group B, ‘Senior Citizen’ tickets were purchased at a 20% discount, while tickets under the other two categories were purchased at the original prices. For Group C, ‘Child’ tickets were purchased at half the ‘Adult’ original price, while ‘Senior Citizen’ and ‘Adult’ tickets were purchased at the original prices. The numbers in each age category for each group and the total price of the tickets for each group, are given in the following table.

Group	Senior Citizen	Adult	Child	Total Price
A	5	12	6	$2440
B	15	10	5	$2660
C	8	10	12	$2560

(a)Express this information as 3 linear equations and hence find the original price of a ticket in each of the age categories. [3]

(b)The Lee family, consisting of 2 senior citizens, 2 adults and 3 children, went to the concert. Assuming their tickets were purchased at the original prices, find the total price they paid. [1]

Show full worked solution▾

(a)Let $x$ , $y$ , $z$ be the original price ($) of a ticket for ‘Senior Citizen’, ‘Adult’ and ‘Child’ respectively.

$5x+12y+6z=2440$ — (1)

$15(0.8)x+10y+5z=2660$

$12x+10y+5z=2660$ — (2)

$8x+10y+12\left(\dfrac y2\right)=2560$

$8x+16y=2560$ — (3)GC, $x=80$ , $y=120$ and $z=100$ .original price of a ticket for ‘Senior Citizen’, ‘Adult’ and ‘Children’ is $80, $120 and $100 respectively.

(b) $2(80)+2(120)+3(100)=700$ family spends $700.

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