Question

A crew consists of 1 apprentice, 1 journeyman, and 1 master carpenter.The crew receives a check for $9200 for a job they just finished. A journeyman makes 300% of what an apprentice makes, and a mmaster makes 250% of what a journeyman makes. Howmuch does each person on the crew cam?

Answer 1

Variables

• x: salary of the apprentice

,

• y: salary of the journeyman

,

• z: salary of the master carpenter

The crew receives a check for $9200, then:

x + y + z = 9200 (eq. 1)

A journeyman makes 300% (3 times) of what an apprentice makes, then:

y = 3x (eq. 2)

A master makes 250% (2.5 times) of what a journeyman makes, then:

z = 2.5y (eq. 3)

Substituting equation 2 into equation 3:

z = 2.5(3x)

z = 7.5x (eq. 4)

Substituting equations 2 and 4 into equation 1:

x + 3x + 7.5x = 9200

Combining similar terms:

11.5x = 9200

Dividing by 11.5 at both sides:

11.5x/11.5 = 9200/11.5

x = 800

Substituting this result into equation 2:

y = 3*800

y = 2400

Substituting x = 800 into equation 4:

z = 7.5*800

z = 6000

Answer

• salary of the apprentice: $800

,

• salary of the journeyman: $2400

,

• salary of the master carpenter: $6000