Katherine is working two summer jobs, making $16 per hour lifeguarding and making $6 per hour walking dogs. In a given week, she can work a maximum of 15 total hours and must earn at least $160. If Katherine worked 2 hours walking dogs, determine the minimum number of whole hours lifeguarding that she must work to meet her requirements. If there are no possible solutions, submit an empty answer.

Answer:Katherine need to work minimum 10 hours lifeguarding to meet her requirementsStep-by-step explanation:Given:Rate for Lifeguarding = [tex]$16\ per\ hour[/tex]Rate for walking dogs = [tex]$6 \ per\ hour[/tex]She had worked 2 hours walking dogMoney for walking dogs = Rate for walking dogs[tex]\times[/tex] hours worked=[tex]\$6\times2=\$12[/tex]she can work a maximum of 15 total hours and must earn at least $160.Let hours required for lifeguarding be xMoney for life guarding = Rate for walking dogs[tex]\times[/tex] hours worked for lifrguarding= [tex]\$16 \timesx=16x[/tex]Total Money she must earn = Money for lifeguarding + Money for walking dogs [tex]16x+12=160\\16x=160-12\\16x=148\\x=\frac{148}{16}=9.25 \ hours[/tex]Rounding to nearest hour Katherine need to work minimum 10 hours lifeguarding to meet her requirements