Some students are taking a math contest in which each student takes one of four tests. One third of the students take the first test, one fo

Question

Some students are taking a math contest in which each student takes one of four tests. One third of the students take the first test, one fourth take the second test,
one fifth take the third test, and 26 students take the fourth test. How many students
are taking the contest in total?

PLS GIVE EXPLANATION !!!

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Eirian 6 months 2021-08-04T07:08:49+00:00 1 Answers 7 views 0

Answers ( )

    0
    2021-08-04T07:10:18+00:00

    Answer:

    120

    Step-by-step explanation:

    Let x students are taking the contest in total.

    According to the given information:

     \frac{1}{3} x +  \frac{1}{4} x +  \frac{1}{5} x + 26 = x \\  \\ (LCM \: of \: 3, \: 4, \: 5 = 60) \\   \\ \frac{20}{60} x +  \frac{15}{60} x +  \frac{12}{60} x + 26 = x  \\  \\ \frac{(20 + 15 + 12)}{60} x    + 26 = x  \\  \\ \frac{47}{60} x    + 26 = x  \\  \\ 26 =  x - \frac{47}{60} x \\  \\ 26 =  \frac{60x - 47x}{60}  \\  \\ 26 =  \frac{13}{60} x \\  \\  \cancel{26} \times  \frac{60}{ \cancel{13}}  = x \\  \\ 2 \times 60 = x \\  \\ x = 120

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