SOLUTION: Please help me solve this word problem.... A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 3 gallons of a mixture that is 30 parts gasoline a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this word problem.... A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 3 gallons of a mixture that is 30 parts gasoline a      Log On


   

Question 988509: Please help me solve this word problem....
A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 3 gallons of a mixture that is 30 parts gasoline and 1 part oil. How many gallons of gasoline should the forester add to bring the mixture to 50 parts gasoline and 1 part oil?
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Take the viewpoint of fraction as gasoline.
Your forester wants 50%2F51 gasoline result.

Let g be the amount of gasoline in gallons to add.
%283%2830%2F31%29%2Bg%29%2F%283%2Bg%29=50%2F51

If the equation makes sense, then next need just solve for g.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of gasoline to be added
so that [ gasoline ] / [ oil ] = +50%2F1+
------------------------------------
To start with:
[ gasoline] / [ oil ] = +30%2F1+
The gasoline is +3%2A%28+30%2F%28+30+%2B+1+%29+%29+=+90%2F31+ gallons
The oil is +3%2A%28+1%2F%28+30+%2B+1+%29%29+=+3%2F31+ gallons
-------------------------------------
Note that +90%2F31+%2B+3%2F31+=+93%2F31+ and
+93%2F31+=+3+ gallons as it should
-------------------------------------
I can say:
+%28+90%2F31+%2B+x+%29+%2F+%28+3%2F31+%29+=+50%2F1+
+90%2F31+%2B+x+=+%283%2F31%29%2A50+
+x+=+150%2F31+-+90%2F31+
+x+=+60%2F31+
60/31 gallons of gasoline must be added to mixture
-------------------
check:
+%28+90%2F31+%2B+x+%29+%2F+%28+3%2F31+%29+=+50%2F1+
+%28+90%2F31+%2B+60%2F31+%29+%2F+%28+3%2F31+%29+=+50%2F1+
Multiply top anfd bottom of left side by +31+
+%28+90+%2B+60+%29+%2F+3+=+50+
+150+=+150+
OK
hope I got it

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!


Mixture: 3 gallons of 30:1 (gasoline to oil)
Please help me solve this word problem....
A forester is making a gasoline-oil mixture for a chainsaw engine. The forester has 3 gallons of a mixture that is 30 parts gasoline and 1 part oil. How many gallons of gasoline should the forester add to bring the mixture to 50 parts gasoline and 1 part oil? 
Let the multiplicative factor be x

Then, 30x + x = 3

31x = 3

x+=+3%2F31

Amount of gasoline: 30%283%2F31%29, or 90%2F31

Amount of oil: 3%2F31



Let amount of gasoline to add, be G

Then: %2890%2F31+%2B+G%29%2F%283%2F31%29+=+50%2F1

%28%2890+%2B+31G%29%2F31%29+%2A+%2831%2F3%29+=+50

%28%2890+%2B+31G%29%2Fcross%2831%29%29+%2A+%28cross%2831%29%2F3%29+=+50

%2890+%2B+31G%29%2F3+=+50

90 + 31G = 150 ---- Cross-multiplying

31G = 150 - 90

31G = 60

G, or gas to add = highlight_green%2860%2F31%29 gallons