To represent the given real-world situation as an algebraic equation, let's break down the information provided:
1. Variables:
- Let [tex]\( f \)[/tex] be the number of thingamabobs.
- Let [tex]\( w \)[/tex] be the number of whatzits.
2. Values:
- Ariel gets [tex]$3 for each thingamabob.
- Ariel gets $[/tex]8 for each whatzit.
3. Total money:
- The total money Ariel gets from selling the thingamabobs and whatzits is [tex]$55.
To form an equation from this information, we need to express the total earnings from selling the thingamabobs and whatzits and set it equal to $[/tex]55.
- The total money from thingamabobs is [tex]\( 3f \)[/tex] (since each thingamabob is worth [tex]$3 and there are \( f \) thingamabobs).
- The total money from whatzits is \( 8w \) (since each whatzit is worth $[/tex]8 and there are [tex]\( w \)[/tex] whatzits).
When we add these together, we get the total money from selling both types of artifacts:
[tex]\[ 3f + 8w \][/tex]
Since her total earnings are $55, we set up the equation:
[tex]\[ 3f + 8w = 55 \][/tex]
So, the algebraic equation that represents this relationship is:
[tex]\[ 3f+8w=55 \][/tex]
