Thread: Help with mixture word problem

1. Help with mixture word problem

I have some difficulties with mixture word problems. In one of the problems in the book the question was the following:

A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank holds 100 gal. of a solution of 2% ordinary household bleach mixed with pure distilled water.. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

So what I did was this, I set up the following equation:

100(.02) - (.02x) + (x) = 100(0.05)

I then solved for x and got the correct answer. Now another question asks this question:

The radiator in a car is filled with a solution of 60% antifreeze and 40% water.The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6 L how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?

So I set up my equation like the one above and got this:

3.6(.6) - (.06x) + (x) = 3.6(.5)

In the end once I solved for x, the answer I got was a negative and wrong. Can someone please explain to me where I keep going wrong? Thanks

2. Originally Posted by coolieman
I have some difficulties with mixture word problems. In one of the problems in the book the question was the following:

A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank holds 100 gal. of a solution of 2% ordinary household bleach mixed with pure distilled water.. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

So what I did was this, I set up the following equation:

100(.02) - (.02x) + (x) = 100(0.05)

I then solved for x and got the correct answer. Now another question asks this question:

The radiator in a car is filled with a solution of 60% antifreeze and 40% water.The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6 L how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level?

So I set up my equation like the one above and got this:

3.6(.6) - (.06x) + (x) = 3.6(.5)

In the end once I solved for x, the answer I got was a negative and wrong. Can someone please explain to me where I keep going wrong? Thanks
Because in the second problem you are adding water, not antifreeze. Your equation is set up to find out how much antifreeze you need to add and you need to reduce the concentration of antifreeze, not increase it (like you did in the first problem.)

So track how much water you have, not antifreeze:
$\displaystyle 3.6 \cdot .4 - 0.4x + x = 3.6 \cdot .5$

-Dan