Question

Jerry is experimenting with chemicals in the laboratory. He mixes a solution that is 10% acid with a solution that is 30% acid. How much of the 30% acid solution will be needed to make 40 liters of solution that is 25% acid?

Answer 1

any ideas?

Answer 2

not really i suck at algebra

Answer 3

if you keep telling yourself that then you will!

let's see if i can help you with this problem...

first, what do we want to know?

Answer 4

i guess your right ive just never been able to work out any algebra problems....ok what i would like to know is what opporation am i working with

Answer 5

this is what's called a mixture problem. it's an application of linear systems. read the question and determine what the question is asking for

Answer 6

idk really what its asking for ive read it like 100 times before, and i get lost

Answer 7

well, it's asking for the number of liters of 30% solution. so that will be the variable and we'll define it and use it to write some equations. we'll be writing 2 equations, 1 for the total amount of solution and 1 for the total amount of acid.

let x = the number of liters of 30% solution.

then x + (40-x) = 40 where x is as defined above, (40-x) is the number of liters of 10% acid solution and 40 is the total liters of solution we get.

for the acid total, we get

.30x + .10(40-x) = .25(40)

the first term is the amount of acid the 30% solution contributes to the total, the second term is the amount of acid the 10% solution contributes to the total and the last term is the total amount of acid.

this is a system of 2 linear equations. you can use substitution to solve

Answer 8

i dont really know how to use substitution

Answer 9

give me a minute... i'll be back

Answer 10

ok

Answer 11

actually, because of how we set up the problem we should be able to solve for x directly in the second equation.

so solve the second equation for x.

Answer 12

the second equation is what confused me