Question

understanding representing a situation with different expressions
complete the problems by rewriting algebraic expressions.
1 goby fish and shrimp naturally live close together. a pet store is selling bags of goby fish and shrimp to aquarium hobbyists. each goby fish costs $15, and each shrimp costs $10. each bag has an equal number of goby fish and shrimp.
a. the pet store models the cost per bag with the expression ( x(15 + 10) ). explain what the expression represents.
b. what other expression can you use to model the cost? explain what the expression represents.

Explanation:

a. The expression $x(15 + 10)$ uses the distributive property: $x$ is the number of pairs (goby + shrimp), $15$ is the cost of one goby, and $10$ is the cost of one shrimp. So $15 + 10$ represents the cost of one goby plus one shrimp.
b. Using the distributive property, $x(15 + 10) = 15x + 10x$, which simplifies to $25x$. Both expressions model the total cost: $15x$ is the total cost of gobies, $10x$ is the total cost of shrimp, and their sum (or $25x$) is the total cost per bag.

Answer:

a. Cost of one goby fish plus one shrimp
b. $15x + 10x$ or $25x$