These make my brain hurt. I heard there are two kinds of people who get math. The ones that understand it and also are capable of 'original math thinking' and the ones that can understand after it has been explained over and over again. The ones that need the explaining get by through the memorization of equations that fit a certain type of problem. I'm in the latter group and the following question deviates from the original example so much that I could literally spend hours on it and not get the answer.
Here's two questions for any original thinker who is up for the challenge. If you can please break down your answer step by step.
1.) A grocer mixes two kinds of nuts that cost $2.49 and $3.89 per pound to make a 100 pounds of a mixture that costs $3.47 per pound. How many pounds of each kind of nut are put into the mixture?
2.) The cooling system in a truck contains 4 gallons of coolant that is 30% antifreeze. How much must be withdrawn and replaced with 100% antifreeze to bring the coolant in the system to 50% antifreeze?
These may seem like no brainers to some people. They give me a real headache and I cringe every time I read a problem like this.
Thanks in advance for your help.