Answer :
To solve this problem, we need to find out which equation correctly represents the situation described. Let's break it down step by step:
1. Identify the variables:
- Let [tex]$x$[/tex] represent the number of dozens of roses.
- Let [tex]$y$[/tex] represent the number of dozens of carnations.
2. Determine the cost per dozen for each type of flower:
- Each dozen roses costs [tex]$16.
- Each dozen carnations costs $[/tex]9.
3. Write the expression for the total cost:
The florist buys [tex]$x$[/tex] dozen roses and [tex]$y$[/tex] dozen carnations. So the cost of roses is [tex]$16 per dozen times $[/tex]x[tex]$ dozens, which gives us $[/tex]16x[tex]$. Similarly, the cost of carnations is $[/tex]9 per dozen times [tex]$y$[/tex] dozens, which gives us [tex]$9y$[/tex].
4. Set up the equation for the total amount paid:
We know that the total cost the florist pays is $218. So, the equation representing this situation is:
[tex]\[ 16x + 9y = 218 \][/tex]
This equation correctly reflects the total amount the florist spends on the roses and carnations combined. Thus, the correct choice is:
[tex]\[ 16x + 9y = 218 \][/tex]
This is the equation describing the situation based on the given costs and total expenditure.
1. Identify the variables:
- Let [tex]$x$[/tex] represent the number of dozens of roses.
- Let [tex]$y$[/tex] represent the number of dozens of carnations.
2. Determine the cost per dozen for each type of flower:
- Each dozen roses costs [tex]$16.
- Each dozen carnations costs $[/tex]9.
3. Write the expression for the total cost:
The florist buys [tex]$x$[/tex] dozen roses and [tex]$y$[/tex] dozen carnations. So the cost of roses is [tex]$16 per dozen times $[/tex]x[tex]$ dozens, which gives us $[/tex]16x[tex]$. Similarly, the cost of carnations is $[/tex]9 per dozen times [tex]$y$[/tex] dozens, which gives us [tex]$9y$[/tex].
4. Set up the equation for the total amount paid:
We know that the total cost the florist pays is $218. So, the equation representing this situation is:
[tex]\[ 16x + 9y = 218 \][/tex]
This equation correctly reflects the total amount the florist spends on the roses and carnations combined. Thus, the correct choice is:
[tex]\[ 16x + 9y = 218 \][/tex]
This is the equation describing the situation based on the given costs and total expenditure.
