Question 988509



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? 
<pre>Let the multiplicative factor be x
Then, 30x + x = 3
31x = 3
{{{x = 3/31}}}
Amount of gasoline: {{{30(3/31)}}}, or {{{90/31}}}
Amount of oil: {{{3/31}}}

Let amount of gasoline to add, be G
Then: {{{(90/31 + G)/(3/31) = 50/1}}}
{{{((90 + 31G)/31) * (31/3) = 50}}}
{{{((90 + 31G)/cross(31)) * (cross(31)/3) = 50}}}
{{{(90 + 31G)/3 = 50}}}
90 + 31G = 150 ---- Cross-multiplying
31G = 150 - 90
31G = 60
G, or gas to add = {{{highlight_green(60/31)}}} gallons