Question

Help please...Solve the following problem by writing a system of equations: A 25% alcohol solution is to be mixed with a 45% alcohol solution to obtain 8 liters of a 35% alcohol solution. How many liters of each solution should be used?

Answer 1

65%x=35%(8)
65/100x=2.8
x=4.3 liters

Answer 2

Wait a min I think im wrong
(25%+45%)x=35%(8)
.7x=2.8
X=4 liters
At first I added wrong

Answer 3

hmmm

Answer 4

lets call \(x\) the amount of 45% solution, so it will contain \(.45x\) alcohol
then the amount of 25% solution must be \(8-x\) because the total is 8
it will contain \(.25(x-8)\) alcohol
the total will therefore be
\[.45x+.25(8-x)\] and you want that to be 35% of 8 which is 2.8 so set
\[.45x+.25(8-x)=2.8\] and solve for \(x\)

Answer 5

probably be easier to solve
\[45x+25(8-x)=280\]for \(x\) because decimals are annoying

Answer 6

@ktnguyen1 got the correct answer, but that was coincidence. just so happened the amounts were equal, which is what he/she assumed before writing the equation

Answer 7

I see now...I ended up getting the 2.8, but was not sure if it was the correct answer. So this is only solving by one variable not two for x and y?

Answer 8

Would solving for two variables be like my next problem: A car leaves St. Paul, Minnesota at 4 pm. A bus leaves the same place at 5 pm and travels in the same direction as the car. The car is traveling 12 mph faster than the bus. At 8 pm the vehicles are 100 miles apart. What is the speed of each car?

Answer 9

i think we can do this

Answer 10

lets call the rate of the car \(x\) so the rate of the bus is \(x-12\) because it is slower
since distance is rate times time, we know the distance the car travelled is \(4x\) and the distance the bus travelled is \(3(x-12)\)
the first distance is 100 miles more than the second distance, so ste
\[4x=3(x-12)+100\] and solve for \(x\)

Answer 11

this one is pretty easy to solve you get
\[4x=3x-36+100\]
\[4x=3x+64\]
\[x=64\]

Answer 12

Oh, ok I think I get it now. Thank you for your help!