Question

Drag and drop numbers into the boxes to complete and solve the equation for the situation. One month, Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hours. Find the number of hours each person worked. h + parenleftzeh + parenrightze + parenleftzeh + parenrightze = 126 Isaac worked hours. Ruby worked hours. Svetlana worked hours.

Answer 1

Ruby = x = 22 hours

Isaac = y = 16 hours

Svetlana = 88 hours

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