Answer:
Ruby = x = 22 hours
Isaac = y = 16 hours
Svetlana = 88 hours
Step-by-step explanation:
Let the number of hours worked be represented as:
Ruby = x
Isaac = y
Svetlana = z
Total number of hours worked =
x + y + z = 126 hours........ Equation 1
Ruby worked 6 hours more than Isaac,
x = y + 6..... Equation 2
Svetlana worked 4 times as many hours as Ruby
z = 4 × x
z = 4x
z = 4(y + 6)
z = 4y + 24....... Equation 3
Substituting y + 6 for x and 4y + 24 for z in Equation 1
x + y + z = 126 hours........ Equation 1
y + 6 + y + 4y + 24 = 126
Collect like terms
y + y + 4y + 6 + 24 = 126
6y + 30 = 126
6y = 126 - 30
6y = 96
Divide both sides by 6
6y/6 = 96/6
y = 16
Since y represents the number of hours Isaac worked, Isaac worked for 16 hours
Substitute 16 for y in equation 2
x = y + 6
x = 16 + 6
x = 22
Since x represents the number of hours Ruby worked, Ruby worked for 22 hours
Substitute 16 for y in equation 3
z = 4y + 24
z = 4 × 16 + 24
z = 64 + 24
z = 88
Since z represents the number of hours Svetlana worked, Svetlana worked for 88 hours
Therefore:
Ruby worked for 22 hours
Isaac worked for 16 hours
Svetlana worked for 88 hours
