Simultaneous equations
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1
Two families go to a magic show.
Family 1 buys 4 adult tickets and 3 child tickets; they pay £23.10.
a Write down an equation to illustrate this.
1 Marks
Family 2 buys 3 adult tickets and 5 child tickets, they pay £24.20.
b Write down an equation to illustrate this.
1 Marks
c Calculate the cost of an adult and a child ticket.
3 Marks
Show Answer
Adult £3.90
Child £2.50
2
Two families go to a concert
Joe buys 3 adult tickets and 7 child tickets; they pay £49.20.
a Write down an equation to illustrate this.
1 Marks
Sandy buys 2 adult tickets and 5 child tickets for £34.80
b Write down an equation to illustrate this.
1 Marks
c Calculate the cost of an adult and a child ticket.
3 Marks
Show Answer
Adult £6
Child £2.40
3
Solve algebraically
3x + 4y = 24
5x + 3y = 29
3 Marks
Show Answer
x = 4
y = 3
4
Solve algebraically
5x + 3y = 34
4x + 5y = 22
3 Marks
Show Answer
x = 8
y = -2
5
The graph below shows two straight lines
The lines have equations 3x + 2y = 4
and 4x + 3y = 7
The lines intersect at point A.
Find algebraically the coordinates of point A
4 Marks
Show Answer
x = -2
y = 5
6
Two groups of people go ice skating.
Sally pays entry for 5 adults and 3 children.
The total cost of entry is £42.25
a Write down an equation to illustrate this.
1 Marks
Jim pays entry for 3 adults and 2 children, the total cost of entry is £26.
b Write down an equation to illustrate this.
1 Marks
c Algebraically, calculate the price of entry for an adult and the price of entry for a child.
4 Marks
Show Answer
Adult £6.50
Child £3.25
7
Kenny is renovating his garden.
On his first journey to the garden centre, he buys 5 bags of topsoil and 3 bags of sand for £45.25.
a Write an equation to illustrate this.
1 Marks
On his second journey to the garden centre, he buys 3 bags of topsoil and 4 bags of sand for £36.50
b Write an equation to illustrate this.
1 Marks
c Algebraically, calculate the cost of a bag of topsoil and the cost of a bag of sand.
4 Marks
Show Answer
Topsoil £6.50
Sand £4.25