word problem

Question

The octane rating of gasoline is a measure of the amount of isoocatane in a gallon of gas. Subaru recommends 91-octane gasoline for the 2009 legacy 30. R. How much 87-octane gas and how much 93-octane gas should be mix in order to make 12 gal of 91-octane gas for the legacy

Answer 1

x=# of gallons  of 87 octane

y=# of gallons of 93 octane

87x+93y=12(91)

x+y=12

x=12-y

87(12-y)+93y=1092

1044-87y+93y=1092

1044+6y=1092

6y=1092-1044

6y=48

y=8 gallons of 93 octane

x=4 gallons of 87 octane

 

another simpler solution...

87x+93y=12(91)

x+y=12

87x+93y=(x+y)(91) because (x+y)=12

87x+93y=91x+91y

93y-91y=91x-87x

2y=4x

y=2x means the number of gallons of 93 octane is twice the number of gallons of 87 octane

seeing you have 12 gallons, 8+4=12 and 8 is two times 4

however, a more complicated problem warrants the use of a more complicated solution such as two simultaneous linear equations