The sum of three numbers is 27. The product of the first number times the third number is 56. The quotient of the second number divided by the first number is 1.5. If the first number is represented by x, the second number is represented by y, and the third number is represented by z, which of the systems of equations below can be used to determine the three numbers?

The system of equations that can be used to determine the three numbers are equation 1 and 6

x + y + z = 27 ( 1 )

37.33 x - 56 y + 0 = 0   ( 6 )

Step-by-step explanation:

x + y + z = 27 ( 1 )

x * z = 56 ( 2 )

y / x  = 1.5   ( 3 )

from equation 3

x = y / 1.5   ( 4 )

input equation 4 into ( 2 )

( y / 1.5 ) * z = 56

y * z = 37.33  ( 5 )

from equation 5 ;  z = 37.33 / y input  back to equation 2

x ( 37.33 / y ) = 56

37.33 x = 56 y  

37.33 x - 56 y  + 0 = 0   ( 6 )

step-by-step explanation: