Find the number of hours worked

Ryan is working his way through school. He works two part-time jobs for a total of 26 hours a week. Job A pays $6.20 per hour, and Job B pays $6.90 per hour. How many hours did he work at each job the week that he made $168.90

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a = number of hours at job A
b = number of hours at job B

a + b = 26  {works two jobs for a total of 26 hours}
6.2a + 6.9b = 168.9  {$6.20 for job a and $6.90 for job B, with a total of $168.90}

a + b = 26  {first equation}
a = -b + 26  {subtracted b from each side of first equation}

6.2a + 6.9b = 168.9  {second equation}
6.2(-b + 26) + 6.9b = 168.9  {substituted (-b + 26), in for a, into second equation}
-6.2b + 161.2 + 6.9b = 168.9  {used distributive property}
0.7b + 161.2 = 168.9  {combined like terms}
0.7b = 7.7  {subtracted 161.2 from each side}
b = 11  {divided each side by 0.7}

a + b = 26  {first equation}
a + 11 = 26   {substituted 11, in for b, into first equation}
a = 15   {subtracted 11 from each side}

15 hours at job A
11 hours at job B

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