I Love Musical Stars
Age
14 to 16
Challenge level
Each row and column has the total given. What is the value of the heart symbol?
Problem
What is the value of
Image
if each row and column has the given totals?
Image
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $3$
Substitution
Image
So 2
Image
are worth 2 more than 2
Image
Image
3
Image
would be worth 2 less ie. 9, so each
Image
is worth 3.
Elimination
Consider the third column:
$2$
Image
$+$
Image
$=13$ $(1)$
and the second row:
Image
$+ 2$
Image
$=11$ $(2)$
$2 \times (2) - (1)$ yields:
$3$
Image
$=9$
So
Image
$=3$.