Algebra 1 question help

Question

Jenny worked five hours less than twice as many hours as Philip. Jenny earned 15 dollars per hour as team leader and Philip earned 8 dollars per hour as a line worker. together Jenny and Philip earned 685 dollars. how many hours did each person work? Solve with Elimination.

Answer 1

Let’s assume Jenny worked J hours and Philip worked P hours. As problem says:

J=2*P-5

They together made $685 at the rate of $15 for Jenny, and $8 for Philip, so

15*J+8*P=685

solving this system of equations shows Philip worked 20 hours, and Jenny worked 35 hours. 

 

Now let’s solve using elimination method (matrix form). First rearrange system of equations as given below:

 

15*J+8*P=685

J-2*P=-5

 

now set the matrix (call this as original matrix)

[15     8    . 685

  1     -2    . -5]       

Note: it is a 2by3 matrix, and we want to make it upper or lower triangle by just working on 15 and 8 from first row, 1 and -2 from second row (that is why I put dots before -5 and 685. So, we have the following matrix (call it as solution matrix)

[15     8

  1      -2]

by multiplying the second row by 4 and adding it to the second line we can make a lower triangle as below. (In fact we eliminate one element from matrix)

[19      0
 1        -2]

 

keep in mind the same thing will happens to the original matrix as well. In other words we multiply -5 by 4 and it add to 685 which gives 665. Then the original matrix changes as below

[19      0       .665

  1        -2     . -5  ]

so Jenny worked 665/19=35 and from ther Philip worked 20 hours.

 

i have to explain in details, but it is easy and I solved in two dofferent ways, but it seems you need the second solution (elimination).

Let me know if there is some point you need more explanation.

 

Answer 2

First identify the quantities involved.
J = hours worked by Jenny
P = hours worked by Philip
Then write the formulas that relate them
J = 2P - 5
15J + 8P = 685
Substitute for J and solve for P
15(2P -5) + 8P =685
30P-75 + 8P = 685
38P = 685+75 = 760
P = 20
Substitute for P and solve for J
J = 2*20