System of Equations : Word Problems
PLease explain how to get this answer.
Judy worked 8 hours and Ben 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person.
PLease explain how to get this answer.
Judy worked 8 hours and Ben 10 hours. Their combined pay was $80. When Judy worked 9 hours and Ben worked 5 hours, their combined pay was $65. Find the hourly rate of pay for each person.
Let Judy's hourly wage =J
Let Ben's hourly wage =B
8J + 10B=80,
9J + 5B =65
Solve the following system:
{5 B+9 J = 65 | (equation 1)
10 B+8 J = 80 | (equation 2)
Swap equation 1 with equation 2:
{10 B+8 J = 80 | (equation 1)
5 B+9 J = 65 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{10 B+8 J = 80 | (equation 1)
0 B+5 J = 25 | (equation 2)
Divide equation 1 by 2:
{5 B+4 J = 40 | (equation 1)
0 B+5 J = 25 | (equation 2)
Divide equation 2 by 5:
{5 B+4 J = 40 | (equation 1)
0 B+J = 5 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{5 B+0 J = 20 | (equation 1)
0 B+J = 5 | (equation 2)
Divide equation 1 by 5:
{B+0 J = 4 | (equation 1)
0 B+J = 5 | (equation 2)
Collect results:
Answer: | B = 4 and J=5
