Carrie has c dollars and Marjani has m dollars. Carrie has 3 times as many dollars as Marjani, and together they have a total of 28.00. Which system of equations represents this situation?

Carrie has c dollars and Marjani has m dollars. Carrie has 3 times as many dollars as... | SAT Systems of two linear equations in two variables Practice

Answer: A. $c=3m$ ; $c+m=28$

Explanation:1. Define the variables: - Carrie has $c$ dollars. - Marjani has $m$ dollars.

Translate the given statements into equations: - Statement 1: "Carrie has $3$ times as many dollars as Marjani." This translates to $c = 3m$ .

Statement 2: "together they have a total of $ $28.00$ ." This translates to $c + m = 28$ . (Assuming the $ $28.00$ means $28$ dollars).

Combine the equations to form a system: The system of equations is: Equation 1: $c = 3m$ Equation 2: $c + m = 28$
Compare this system with the given options: - [A] $c=3m$ ; $c+m=28$ (This matches our system). - [B] $m=3c$ ; $c+m=28$ (Equation 1 is incorrect; this would mean Marjani has $3$ times as many dollars as Carrie). - [C] $c=28m$ ; $c+m=3$ (Both equations are incorrect based on the statements). - [D] $m=28c$ ; $c+m=3$ (Both equations are incorrect based on the statements).
Conclusion: The system of equations that represents this situation is $c=3m$ and $c+m=28$ .