Solution
From the stem we are able to form an equation:
\(6x + 24y = 126\) ornaments
we are asked to solve for yWe can simplify this equation to \(x + 4y = 21\) but remember that x and y must be integers as they relate to whole boxes.
(1) Fewer than 4 boxes contain 6 ornaments
let's test values
\(x = 3
3 + 4y = 21
4y = 18\)
18 is not divisible by 4 , x=3 is not a solution
\(x=2
2 + 4y = 21
4y = 19\)
again, not a solution
\(x=1\) (the last value we can test)
\(1 + 4y = 21
4y = 20
y = 5\)
This is the only possible solution.
\((1)--> Sufficient\)
(2) More than 3 boxes contained 24 ornaments
This tells us \(y > 3\)
Let's test values for y using the original equation \(6x + 24y =126\)
\(y = 4
6x + 24(4) = 126
6x = 54
x = 9\)
one possible solution
\(y = 5
6x + 24(5) = 126
6x = 6
x= 1\)
Another possible solution
2 possible answers for x--> Inconsistent therefore
\(Insufficient\)