Linear equations with 2 variables, word problems

[NotGoodWithNumbers]

I'm having trouble trying to figure these out. if anyone can help me on any 1 it would be greatly appreciated. here are the problems




Mara needs to mix some 30% acid solution and some 70% alcohol solution to end up with 20 liters of 54% solution. How many liters of the 70% solution will she need?





One serving of soybeans contains 14 grams of protein and 8 grams of fat. One serving of rice contains 4 grams of protein and 1/2 gram of fat. Calculate the number of servings of each that need to be combined, in order to end up with precisely 30 grams of protein and 15 grams of fat. How many servings of rice will be needed?




Ken invests $6,000 into two accounts. One account earns 8% interest and the other earns 12% interest. After one year his total interest earned from the two accounts totals $580. How much did Ken invest in the 8% account?

Two types of tickets are sold for a concert. Adult tickets cost $10 each, while a child's ticket costs $6. A total of 190 tickets are sold, bringing in a total of $1,740. How many adult tickets were sold?

 

[pka]

For your acid problem solve this:
x+y=20 (the total volume)
(0.3)x+(0.7)y=(0.54)(20) (the total amount of acid).

 

[tkhunny]

Ken invests $6,000 into two accounts. One account earns 8% interest and the other earns 12% interest. After one year his total interest earned from the two accounts totals $580. How much did Ken invest in the 8% account?

Name Stuff!
Name what?
What does it want?
"How much did Ken invest in the 8% account?"
Name that.

x = Amount invested @ 8%

That's all you need. Now, do some pondering.

$6000 - x = Amount invested @ 12%

Recall I = P*r*t

"After one year"
t = 1

x*0.08*1 + ($6000-x)*0.12*1 = $580
x*0.08 + ($6000-x)*0.12 = $580

Can you take it from there?