Answer
Number of roses $=6$.
Number of carnations $=14$.
Work Step by Step
Let the number of roses $=x$.
and the number of carnations $=y$.
Total flowers and carnations $=20$.
$\Rightarrow x+y=20$...... (1)
Cost of $x$ roses $=3x$.
Cost of $y$ roses $=1.50y$
Total cost $=\$39$.
$\Rightarrow 3x+1.50y=39$......(2)
Multiply equation (1) by $-3$.
$\Rightarrow -3(x+y)=-3(20)$
Apply distributive peroperty.
$\Rightarrow -3x-3y=-60$...... (3)
Add equation (2) and (3).
$\Rightarrow 3x+1.50y-3x-3y=39-60$
Simplify.
$\Rightarrow -1.50y=-21 $
Divide both sides by $-1.50$.
$\Rightarrow \frac{-1.50y}{-1.50}=\frac{-21}{-1.50} $
Simplify.
$\Rightarrow y=14$.
Substitute the value of $14$ into equation (1).
$\Rightarrow x+14=20$
Subtract $14$ form both sides.
$\Rightarrow x+14-14=20-14$
Simplify.
$\Rightarrow x=6$
