Word problems! Help :P

[Candygirl5134]

Hi, I have a few problems left from my homework that I have gotten stuck on, and just can't figure out how to set them up.

The first is this:
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Gualtemala Antigua blend with the Arabian Mocha blend, but always in the same proportion. Yesterday, you mixed 60 pounds of the Gualtemala Antigua blend with 126 pounds of the Arabian Mocha blend. Today, there is 50 pounds of the Gualtemala Antigua coffee left in stock. How many pounds of the Arabian Mocha coffee should you mix with it to get your secret blend
I don't know what formula to even use to begin setting it up!

Second:
Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 8 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 4784 dollars. How much did she invest at each rate
Because there is no amount of how much she invested, I don't know what to do.

Third:
A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 30 minutes. What is the plane's speed in still air, and how fast is the wind blowing?
This one just baffles me, because I don't remember ever doing anything like it in class.

Any help is greatly appreciated, as you can see word problems really get the best of me!

 

[JeffM]

Hi, I have a few problems left from my homework that I have gotten stuck on, and just can't figure out how to set them up.

The first is this:
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Gualtemala Antigua blend with the Arabian Mocha blend, but always in the same proportion. Yesterday, you mixed 60 pounds of the Gualtemala Antigua blend with 126 pounds of the Arabian Mocha blend. Today, there is 50 pounds of the Gualtemala Antigua coffee left in stock. How many pounds of the Arabian Mocha coffee should you mix with it to get your secret blend
I don't know what formula to even use to begin setting it up!

Second:
Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 8 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 4784 dollars. How much did she invest at each rate
Because there is no amount of how much she invested, I don't know what to do.

Third:
A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour and 30 minutes. What is the plane's speed in still air, and how fast is the wind blowing?
This one just baffles me, because I don't remember ever doing anything like it in class.

Any help is greatly appreciated, as you can see word problems really get the best of me!

OK help (not answers) is what we provide.

We strongly prefer that you post one problem per thread, not three problems in a single thread. Understand for the future?

In EVERY word problem, the FIRST thing to do is to assign a definition and a symbol (letter) to EACH unknown that MAY BE relevant to the problem.

Let's use your first problem as an example. What do you need to find? The weight of the Arabian blend.

\(\displaystyle Let\ a = weight\ of\ Arabian\ blend.\). That is not too hard, is it?

The second step is to take the specific information explicitly given in words or implied in the problem plus any RELEVANT general information that you are expected to know, and to translate that information into mathematical form using the symbols chosen in step 1. This is usually the hard step. In this case, the general information that you are expected to know is that a recipe gives you information about relative proportions. That is, when you read a recipe, you can always make double the amount by doubling everything. You knew that, but it may not have occurred to you. But the problem tells you how to determine the relative proportions of the two types of coffee in this recipe. What is that relative proportion. (It is implied right there in the problem.) OK. So the proportion stays the same. The problem also gives you the weight of the Guatemala blend available today. So what is the proportion today? How do you express that using the symbol a?

Congratulations. You now have an equation. Solving the equation is usually mechanical.

 

[Candygirl5134]

Sorry, I have never posted before! I think I might be able to do it now!