Fuel Mixture: You mix gasoline and oil to obtain 2.5 gals of

[SCSmith]

You mix gasoline and oil to obtain 2 1/2 gallons of mixture for an engine.The mixture is 40 parts gasoline and 1 part two -cycle oil. How much gasoline must be added to bring the mixture to 50 parts gasoline and 1 part oil?

Let x = the amount of gasoline in new mixture.

.40(1) + 5/2(x) = .50(x +1)

.40 + 5/2x = .50x +.50

.40 +5/2x = 1/2x +.50

2x = .10

x= .05

Am I on the right track?

 

[arthur ohlsten]

liquid=2.5 gals

gas.=40/41[2.5gals.]
gas.=100/41 gals

oil=1/41 [2.5 gals]
oil=2.5/41 gals

let x gals of gas be added
liquid=[2.5+x]

gas = 50/51 [2.5+x] gals
oil=2.5/41 gals ( oil quantity doesn't change]

[50/51][2.5+x]+ 2.5/41=2.5+x
50[2.5+x][41] +2.5[51] =51[41][2.5+x]
2050[2.5+x] +127.5 =2091[2.5+x]
5125+2050x +127.5 =5227.5+2091x
25=41x
x=25/41 gals gasoline to be added answer

please check for errors
Arthur

 

[Denis]

since 41 = 2.5gal
then 51 = 2.5 / 41 * 51 = 127.5 / 41

so added is 127.5 / 41 - 2.5
= (127.5 - 102.5) / 41
= 25 / 41

 

[arthur ohlsten]

the amount gas to be added to known quantity of oil is x

gals. of oil=2.5/41
then:
2.5/41 = 1/51[2.5+x]
127.5=41x+102.5
25/41=x gals to be added

Arthur

 

[Denis]

2.5(41 + 10) / 41 - 2.5

= 2.5(51/41 - 1)

= 2.5(10/41)

= 25/41

:roll: