Julio is studying for his final exams in chemistry and algebra. He knows he only has 12 hours to study and it will take him at least 2 more hours to study for algebra than chemistry. The following system of equations represents the situation, where x represents algebra and y represents chemistry: x+y≤12 x≥y+2 Which of the following can Julio do? Study algebra for 7 hours and chemistry for 5 hours Study algebra for 8 hours and chemistry for 4 hours Study algebra for 7 or 8 hours and chemistry for 4 or 5 hours None of the above

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Julio is studying for his final exams in chemistry and algebra. He knows he only has 12 hours to study and it will take him at least 2 more hours to study for algebra than chemistry. The following system of equations represents the situation, where x represents algebra and y represents chemistry:  x+y≤12  x≥y+2  Which of the following can Julio do?  Study algebra for 7 hours and chemistry for 5 hours  Study algebra for 8 hours and chemistry for 4 hours  Study algebra for 7 or 8 hours and chemistry for 4 or 5 hours  None of the above

Clark Carson · Accepted Answer

Let x→ algebra  y→ chemistry  The inequalities are: x+y≤12 (1)  x≥y+2 (2)  From equation (2) we have  −x+y≤−2 (3)  Now salving (1) and (3) we get by taking the equality sign  (1)+(3)  (x+y)+(−x+y)=12+(−2)  ⇒2y=10  ⇒y=5  When y=5 then using x+y=12 we have x=7

Janessa Oneill · Accepted Answer

Given:  x-algebra (study time)  y-chemistry (study time)  x+y≤12 (1)  x≥y+2 (2)  1) algebra 7 hours ⇒x=7  chemistry 5 hours ⇒y=5  Now put x=7 and y=5 in equation (1) and (2)  7+5≤12⇒12≤12 (True)  7≥5+2⇒7≥7 (True)  2) algebra 8 hours ⇒x=8  chemistry 4 hours ⇒y=4  From equation (1) and (2)  8+4≥12⇒12≥12 (True)  8≥4+2⇒8≥6 (True)  This can Julio do  3) algebra 7 or 8 hours ⇒x=7,x=8  chemistry 4 or 5 hours ⇒y=4,y=5  Now 7+4≤12⇒11≤12  7≥4+2⇒7≥6  8+5≤12⇒13≤12(x)  This can not Julio do

Julio is studying for his final exams in chemistry and algebra. He knows he only has 12 hours to stu

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