Juliana M. answered • 09/05/19
BYU chemistry graduate with >2,000 hours of teaching experience
Peter, John, and Job together have $62,000.
If x = the amount of money that Peter gets
y = the amount of money that John gets
z = the amount of money that Job gets,
Then: 62,000 = x + y + z
If Peter gets 3.5 times as much as John, then x = y*3.5
If John gets 1.5 times as much as Job, then y = z*1.5
We can manipulate these equations to express every variable as y multiplied by or divided by something (in other words, putting all the variables in terms of y.
We were given x = y*3.5. For the second expression, since y = z*1.5, then z = y/1.5
If 62,000 = x + y + z, then:
62,000 = (y*3.5) + y + (y/1.5)
62,000 = 4.5y + y/1.5
To make the algebra simpler, we can give everything on the right the same denominator. We do this by multiplying 1.5x4.5 and then setting everything on the right over a common denominator of 1.5.
62,000 = (6.75y/1.5) + (y/1.5)
62,000 = (6.75y + y)/1.5
62,000 = 7.75y/1.5
Multiplying both sides by 1.5 removes the denominator from the right side
93,000 = 7.75y
Now we can divide each side by 7.75 to leave just y by itself on the right side.
y = 12,000
Recall that y = the amount of money that John would get.
Now that we know this, we can find out what x was, because the problem tells us that x = y*3.5 (in other words, Peter received 3.5 times as much money as John did).
x = (12,000)*3.5
x = 42,000
To solve for y, we have two options. Remembering that 62,000 = x + y + z, we could say:
62,000 = 42,000 + 12,000 + z
Subtracting 42,000 and 12,000 from both sides leaves us with
z = 8,000
However, we could also remember that John received 1.5x as much money as Job did. In other words, y = z*1.5
12,000 = z*1.5
Dividing both sides by 1.5 would leave us with
z = 8,000.
As we see, either method would yield the same answer.
