High School

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What is the algebraic sentence that will help Mitch decide how many friends he can treat?

A. [tex]2f + 10 = 24[/tex]
B. [tex]f + 2 + 10 = 24[/tex]
C. [tex]2f - 10 = 24[/tex]
D. [tex]f + 2 - 10 = 24[/tex]

Answer :

Final answer:

To determine how many friends Mitch can treat, we use the algebraic equation 2f + 10 = 24, which takes into account the cost per friend and the total amount available to spend. The answer is option A.

Explanation:

To determine which algebraic sentence Mitch can use to decide how many friends he can treat, we need to look at each equation and interpret its components. To solve for the variable f (the number of friends Mitch can treat), the correct algebraic sentence needs to account for: the cost per friend, additional costs, and the total amount Mitch can spend.

In this context, the equation 2f + 10 = 24 represents Mitch spending $2 per friend and an additional $10 on something else, with $24 being the total amount he can spend. This equation is the only one that combines the cost per friend and a fixed cost in a manner consistent with the problem. The structure of the other equations either does not account for the costs properly or uses incorrect operations.

To solve the equation, we would subtract 10 from both sides to get 2f = 14 and then divide both sides by 2 to find the number of friends f Mitch can treat.

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