Ayouth group and their leaders visited a museum. three adults and six students in one van paid $102 for their admission. two adults and seven students paid $95 for their admission. marcus wrote a system of linear equations to find the price for each adult and student. he found that each student ticket was $12 and each adult ticket was $9. is marcus correct? explain.

  no, Marcus is not correct

  Marcus's numbers do not satisfy the problem statement.

Step-by-step explanation:

Marcus should have written equations like ...

  3a +6s = 102 . . . . . . where a = the adult ticket price, s = student price

  2a +7s = 95

If he were to graph these equations, he might see the result shown below.

__

If he were to solve them by the "elimination" method, he might multiply the first equation by -2/3 and add it to the second.

  -2/3(3a +6s) +(2a +7s) = -2/3(102) +(95)

  -2a -4s +2a +7s = -68 +95

  3s = 27

  s = 9

Using this value in the first equation, Marcus would have ...

  3a +6·9 = 102

  3a = 48 . . . . . . . . . . subtract 54

  a = 16 . . . . . . . . . . . . divide by 3

Each student ticket was $9; each adult ticket was $16.

_____

Check

3·16 +6·9 = 48 +54 = 102 . . . . first van price agrees

2·16 +7·9 = 32 +63 = 95 . . . . . second van price agrees

_____

If Marcus wrote his equations without defining the variables first, he could easily get the adult price and the student price mixed up. If he didn't know his math facts, he could make a mistake in arithmetic at any of a number of places along the line. His final mistake was that he did not check his answer.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

read more on -

step-by-step explanation:

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft