Dan and Makiko started doing their homework at the same time. It took Dan twice as long to finish his homework than Makiko did. If Dan also took $40$ minutes longer than Makiko did, which of the following systems of equations could be used to determine $d$ , the amount of time Dan took to finish his homework in minutes, and $m$ , the amount of time it took Makiko to finish her homework in minutes?

Full solution

Q. Dan and Makiko started doing their homework at the same time. It took Dan twice as long to finish his homework than Makiko did. If Dan also took

40

minutes longer than Makiko did, which of the following systems of equations could be used to determine

d

, the amount of time Dan took to finish his homework in minutes, and

m

, the amount of time it took Makiko to finish her homework in minutes?

Translate into expressions: Translate the given information into mathematical expressions. $\newline$ Dan took twice as long as Makiko, so we can express this as $d = 2m$ . $\newline$ Dan also took $40$ minutes longer than Makiko, which can be expressed as $d = m + 40$ .
Set up equations: Set up the system of equations using the expressions from Step $1$ . $\newline$ We have two equations: $\newline$ $1$ ) $d = 2m$ $\newline$ $2$ ) $d = m + 40$
Check consistency: Check if the system of equations is consistent with the given information. $\newline$ The first equation represents the fact that Dan took twice as long as Makiko. $\newline$ The second equation represents the fact that Dan took $40$ minutes longer than Makiko. $\newline$ Both equations are consistent with the given information.
Write final system: Write down the system of equations as the final answer. $\newline$ The system of equations is: $\newline$ $1$ ) $d = 2m$ $\newline$ $2$ ) $d = m + 40$