SAT Question ece00725: Answer, Explanation & Desmos Solution

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 $ $25.00$ . Which system of equations represents this situation?

110

Difficulty:Easy

$c = 4 m$

$c + m = 25$

$m = 4 c$

$c + m = 25$

$c = 25 m$

$c + m = 4$

$m = 25 c$

$c + m = 4$

Explanation

Correct answer: A.

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 $c = 4 m$ . It's also given that together, Connor and Maria have a total of $ $25.00$ , which can be represented by the equation $c + m = 25$ . Therefore, the system consisting of the equations $c = 4 m$ and $c + m = 25$ represents this situation.

Desmos solution:

Note: Let x represent Maria's dollars and y Connor's dollars, so y=4x and x+y=25 match the situation.

Enter in Desmos:

$y = 4 x$
$x + y = 25$

Reviewed and rewritten by CookSAT

Why the other choices are wrong

Choice B

Choice B is incorrect. The equation $m = 4 c$ 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

Choice C is incorrect. The equation $c = 25 m$ 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 $ $4.00$ , rather than $ $25.00$ .

Choice D

Choice D is incorrect. The equation $m = 25 c$ 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 $ $4.00$ , rather than $ $25.00$ .

SAT Question ece00725: Systems of Linear Equations answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong