a crew consists of 1 apprentice, 1 journeyman and 1 master carpenter. The crew receives a check for $5950 for a job. A journeyman makes 300% of what a apprentice makes, and a master makes 150% of what journeyman makes how much do each person on the crew make?
The apprentice?
The journeyman ?
The master ?
app makes x
journeyman makes 3 x
master makes 4.5 x
8.5 x = 5950
x = 700 etc
To find out how much each person on the crew makes, we can start by assigning a variable to the amount the apprentice makes. Let's call it "A".
Given that a journeyman makes 300% of what an apprentice makes, we can say that the journeyman makes 3A (300% is the same as 3 times).
Similarly, since a master makes 150% of what a journeyman makes, the master makes 1.5 times what the journeyman makes. Therefore, the master makes 1.5(3A) or 4.5A.
Now let's add up the earnings of all three crew members:
Apprentice (A) + Journeyman (3A) + Master (4.5A) = $5950
Combining like terms, we have:
8.5A = $5950
To isolate the variable A, we divide both sides of the equation by 8.5:
A = $5950 / 8.5
Calculating the right-hand side of the equation:
A = $700
So, the apprentice makes $700.
To find the earnings of the journeyman, we can substitute the value of A into the equation for the journeyman's earnings:
Journeyman = 3A = 3 * $700 = $2100
Therefore, the journeyman makes $2100.
Lastly, to find the earnings of the master, we can substitute the value of A into the equation for the master's earnings:
Master = 4.5A = 4.5 * $700 = $3150
Thus, the master makes $3150.
To summarize:
- The apprentice makes $700.
- The journeyman makes $2100.
- The master makes $3150.