Sakura speaks $150$ words per minute on average in Hungarian, and $190$ words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent $5$ minutes total giving both instructions, and spoke $270$ more words in Polish than in Hungarian. $\newline$ How long did Sakura speak in Hungarian, and how long did she speak in Polish? $\newline$ Sakura spoke for $\square$ minutes in Hungarian and for $\square$ minutes in Polish.

Full solution

Q. Sakura speaks

150

words per minute on average in Hungarian, and

190

words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent

5

minutes total giving both instructions, and spoke

270

more words in Polish than in Hungarian.

\newline

How long did Sakura speak in Hungarian, and how long did she speak in Polish?

\newline

Sakura spoke for

\square

minutes in Hungarian and for

\square

minutes in Polish.

Define Equations: Let $x$ be the time Sakura spoke in Hungarian and $y$ be the time she spoke in Polish. We have two equations based on the given information: $150x$ = the number of words spoken in Hungarian, and $190y$ = the number of words spoken in Polish.
Total Time Spoken: We know Sakura spoke for $5$ minutes total, so $x + y = 5$ .
Difference in Words: We also know she spoke $270$ more words in Polish than in Hungarian, so $190y = 150x + 270$ .
Solve System of Equations: Now we have a system of equations: $\newline$ $1$ ) $x + y = 5$ $\newline$ $2$ ) $150x + 270 = 190y$ $\newline$ Let's solve this system.
Express $y$ in terms of $x$ : From equation $1$ ), we can express $y$ in terms of $x$ : $y = 5 - x$ .
Substitute into Equation: Substitute $y = 5 - x$ into equation $2$ : $150x + 270 = 190(5 - x)$ .
Solve for x: Now, let's solve for x: $\newline$ $150x + 270 = 950 - 190x$ $\newline$ $150x + 190x = 950 - 270$ $\newline$ $340x = 680$ .
Find $y$ : Divide both sides by $340$ to find $x$ : $x = \frac{680}{340}$ $x = 2.$
Final Answer: Now we can find $y$ using $y = 5 - x$ : $y = 5 - 2$ $y = 3.$
Final Answer: Now we can find $y$ using $y = 5 - x$ : $\newline$ $y = 5 - 2$ $\newline$ $y = 3$ . So, Sakura spoke for $2$ minutes in Hungarian and for $3$ minutes in Polish.