One month, ruby worked 6 hours more than Isac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 126 hours. Find the number of hours each person worked
Say x is the number of hours Isac worked. Therefore, (x+6) is the number of hours Ruby worked and 4(x+6) is the number of hours Svetlana worked.
x+(x+6)+4(x+6)=126
Now solve for x and then plug the number back into each equation.
An excellent explanation, Allyson!
To solve this problem, we'll use algebraic equations. Let's start by assigning variables to represent the number of hours each person worked.
Let's say Isac worked 'x' hours.
Ruby worked 6 hours more than Isac, so Ruby worked 'x + 6' hours.
Svetlana worked 4 times as many hours as Ruby, so Svetlana worked '4 * (x + 6)' hours.
According to the problem, together they worked 126 hours, so we can write the equation:
x + (x + 6) + 4 * (x + 6) = 126
Let's solve this equation step by step:
1. Distribute the 4 into the expression (x + 6):
x + x + 6 + 4x + 24 = 126
2. Combine like terms:
6x + 36 = 126
3. Subtract 36 from both sides to isolate the variable term:
6x = 90
4. Divide both sides by 6 to solve for x:
x = 15
So, Isac worked 15 hours, Ruby worked 15 + 6 = 21 hours, and Svetlana worked 4 * (15 + 6) = 84 hours.