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Algebra / Systems of two linear equations in two variables Difficulty: Easy

Connor has $c$ dollars and Maria has $m$ dollars. Connor has $4$ times as many dollars as Maria, and together they have a total of $dollar sign 25.00$ . Which system of equations represents this situation?

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Explanation

Choice A is correct. It’s given that Connor has $c$ dollars, Maria has $m$ dollars, and Connor has $4$ times as many dollars as Maria. This can be represented by the equation $c equals 4 m$ . It’s also given that together, Connor and Maria have a total of $dollar sign 25.00$ , which can be represented by the equation $c + m = 25$ . Therefore, the system consisting of the equations $c equals 4 m$ and $c + m = 25$ represents this situation.

Choice B is incorrect. The equation $m equals 4 c$ represents a situation where Maria has $4$ times as many dollars as Connor, rather than the situation where Connor has $4$ times as many dollars as Maria.

Choice C is incorrect. The equation $c equals 25 m$ represents a situation where Connor has $25$ times, rather than $4$ times, as many dollars as Maria. The equation $c + m = 4$ represents a situation where Connor and Maria together have a total of $dollar sign 4.00$ , rather than $dollar sign 25.00$ .

Choice D is incorrect. The equation $m equals 25 c$ represents a situation where Maria has $25$ times as many dollars as Connor, rather than the situation where Connor has $4$ times as many dollars as Maria. The equation $c + m = 4$ represents a situation where Connor and Maria together have a total of $dollar sign 4.00$ , rather than $dollar sign 25.00$ .