mscroggs
.co.uk
mscroggs
.co.uk
blog
puzzles
academic
talks
contact
subscribe
↓ ☰ ↓
subscribe
Loading image...
Puzzles
Algebraic fractions
Source:
UKMT Senior Maths Challenge 2014
Given that
3
x
+
y
x
−
3
y
=
−
1
what is the value of
x
+
3
y
3
x
−
y
?
Show answer & extension
Hide answer & extension
3
x
+
y
x
−
3
y
=
−
1
implies that
3
x
+
y
=
3
y
−
x
2
x
=
y
This means that
x
+
3
y
3
x
−
y
=
x
+
6
x
3
x
−
2
x
=
7
x
x
=
7
Extension
Given that
3
x
+
y
x
−
3
y
=
−
k
what is the value of
x
+
3
y
3
x
−
y
?
For which values of
k
is the answer an integer?
Tags:
algebra
If you enjoyed this puzzle, check out
Sunday Afternoon Maths XXXIV
,
puzzles about
algebra
, or
a random puzzle
.
Archive
Show me a random puzzle
Most recent collections
Advent calendar 2024
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
List of all puzzles
Tags
digits
palindromes
games
coins
medians
addition
probability
volume
geometry
geometric means
dates
square grids
geometric mean
quadrilaterals
averages
multiplication
division
logic
sum to infinity
spheres
axes
trigonometry
books
means
square numbers
crosswords
parabolas
consecutive integers
perfect numbers
crossnumbers
probabilty
pentagons
cards
dominos
irreducible numbers
clocks
dodecagons
quadratics
even numbers
complex numbers
neighbours
odd numbers
hexagons
factorials
ellipses
decahedra
expansions
lines
taxicab geometry
rugby
dice
the only crossnumber
sets
squares
tournaments
money
sport
arrows
prime numbers
floors
area
median
polygons
wordplay
shape
square roots
percentages
grids
balancing
tiling
multiples
cube numbers
powers
digital products
chalkdust crossnumber
cubics
algebra
consecutive numbers
integers
pascal's triangle
products
christmas
fractions
gerrymandering
regular shapes
functions
triangles
advent
menace
symmetry
calculus
elections
chocolate
cryptic clues
ave
bases
determinants
triangle numbers
shapes
proportion
sequences
people maths
perimeter
scales
unit fractions
graphs
mean
range
3d shapes
factors
circles
matrices
coordinates
rectangles
2d shapes
star numbers
numbers
doubling
planes
number
integration
polynomials
binary
tangents
indices
folding tube maps
albgebra
cryptic crossnumbers
numbers grids
time
differentiation
chess
remainders
colouring
speed
angles
digital clocks
surds
sums
combinatorics
routes
partitions
Archive
Show me a random puzzle
▼ show ▼
▲ hide ▲
Most recent collections
Advent calendar 2024
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
List of all puzzles
Tags
the only crossnumber
ellipses
integers
sum to infinity
combinatorics
dodecagons
expansions
square grids
odd numbers
numbers
fractions
tangents
menace
determinants
grids
rugby
surds
balancing
taxicab geometry
triangle numbers
albgebra
coordinates
mean
cubics
star numbers
time
area
medians
triangles
palindromes
volume
perimeter
even numbers
averages
sequences
circles
products
elections
median
functions
routes
quadratics
hexagons
pentagons
chess
floors
multiples
numbers grids
parabolas
partitions
perfect numbers
dates
matrices
indices
wordplay
advent
crosswords
planes
consecutive integers
geometric means
algebra
logic
factors
bases
geometry
ave
colouring
crossnumbers
people maths
number
proportion
sets
unit fractions
sport
decahedra
shapes
tournaments
2d shapes
tiling
regular shapes
shape
factorials
chalkdust crossnumber
gerrymandering
spheres
rectangles
cube numbers
square roots
doubling
scales
folding tube maps
symmetry
games
speed
money
percentages
probability
geometric mean
neighbours
3d shapes
cryptic clues
cards
complex numbers
arrows
digits
lines
range
sums
graphs
division
calculus
coins
differentiation
trigonometry
multiplication
remainders
squares
dice
cryptic crossnumbers
means
books
consecutive numbers
digital clocks
polygons
binary
square numbers
powers
clocks
probabilty
irreducible numbers
christmas
chocolate
quadrilaterals
polynomials
addition
prime numbers
dominos
angles
pascal's triangle
axes
integration
digital products
© Matthew Scroggs 2012–2025