ANSWER
The girls did not break the record
STEP-BY-STEP EXPLANATION:
Given information
[tex]\begin{gathered} Barbara\text{ spent }3\frac{3}{10}\text{ minutes to complete the relay race} \\ \text{Donna spent 2}\frac{4}{5}\text{ minutes to complete the relay race} \\ \text{ Cindy spent x minutes to complete the relay race} \\ \text{ Nicole spent }2\frac{1}{10}\text{ minutes to complete the relay race} \end{gathered}[/tex]From the question provided, the record set by the school is 12 2/5 minutes
The next step is to find the time spent by Cindy in the relay race
[tex]\begin{gathered} 3\frac{3}{10}\text{ + 2}\frac{4}{5}\text{ + x + 2}\frac{1}{10}\text{ = 12}\frac{2}{5} \\ \text{The next process is to convert the mixed fraction into an improper fraction} \\ \frac{33}{10}\text{ + }\frac{14}{5}\text{ + x + }\frac{21}{10}\text{ = }\frac{62}{5} \\ \text{let the co}mmon\text{ denominator be 10} \\ \frac{33\text{ + 14(2) + 10x + (21})}{10}\text{ = }\frac{62}{5} \\ \frac{33\text{ + 28 + 10x }+\text{ 21}}{10}\text{ = }\frac{62}{5} \\ \frac{82\text{ + 10x}}{10\text{ }}\text{ = }\frac{62}{5} \\ \text{Cross multiply} \\ 5(82\text{ + 10x) = 62 }\times10 \\ 410\text{ + 50x = 620} \\ \text{subtract 830 from both sides} \\ 410\text{ - 410+ 50x = 620 - 4}10 \\ 50x\text{ = 210} \\ \text{Divide both sides by 50} \\ \frac{50x}{50}\text{ = }\frac{210}{50} \\ x\text{ = }\frac{21}{5} \\ x\text{ = 4}\frac{1}{5}\text{ minutes} \end{gathered}[/tex]The next step is to sum all the minutes spent in the relay race
[tex]\begin{gathered} \text{Total minutes =}\frac{33}{10}\text{ + }\frac{14}{5\text{ }}+\frac{21}{5}+\text{ }\frac{21}{10} \\ \text{Total minutes = }\frac{33\text{ + 28 + 42 + 21}}{10} \\ \text{Total minutes = }\frac{124}{10} \\ \text{Total minutes = 12}\frac{4}{10}\text{minutes} \end{gathered}[/tex]From the above calculations, you will see that the girls ran a total of minutes of 12 4/10 minutes
Therefore, the girls did not break the record
