Word problem help, please :(

Question

Sarah needs to prepare 170 pounds of blended coffee beans selling for $5.28 per pound. She plans to do this by blending together a high quality bean costing $6.25 per pound and a cheaper bean at $3.50 per pound. To the nearest pound, find out how much high-quality coffee bean and how much cheaper coffee bean she should blend.

 

Please help me, i've retaken this online thing too many times and I don't know how to do this correctly. 

Answer 1

Hello Devia,

 

As in all word problems, the set-up is the key. Can you write an equation described by the problem above? That's your biggest battle. Doing the algebra that ensues should be easy.

 

What's nice about problems like this is you can check your solution quickly. What are they asking for? Just one of the weights of bean batches, really, since if you know the weight of one batch and you know your total weight, the weight of the other batch is determined for you. So: USE JUST ONE VARIABLE.

 

So, let x be how much high-cost coffee will be used, in pounds. Makes sense, right? (You could just as well use x = weight of low-cost beans. Pick one.)

 

If x = pounds of high-cost beans, and your total pounds of mixed beans will be 170, how much of the low-cost beans will be used?

 

Clue: You don't need another variable!

 

I'm asking you 170 = x + ???

 

What's the ???

 

You'll knock yourself if you didn't get 170 - x. Get it? If x = pounds high-cost beans, then 170-x HAS TO be the pounds of low-cost beans used, because x + (170-x) = 170.

 

Now you're well on the way. It turns out that the amount of coffee in pounds times it's cost per pound equals total cost, right?

 

The 170 pounds beans must average $5.28/pound, so you have a grand total of 170 pounds*($5.28/pound) = $897.60.

 

The rest is just typing it in: x pounds at $6.25/pound + (170-x)pounds at $3.50/pound = $897.60.

 

This is written 6.25*x + 3.50*(170-x) = 897.6, the latter of which happens to be 170*(5.28).

 

With a little bit of calculation, you're at 2.75*x = 897.6 - 595 = 302.6, and x = 302.6/2.75.

 

The amount of high-cost beans is thus just a touch over 110 pounds...I get 110.036 pounds. If you use x = 110.04 pounds, then the weight of low-cost beans would be 59.96 pounds, and your total cost for the 170-pound batch is $897.61, which is close enough!

Word problems. I saw a "Far Side" cartoon once, and it had this guy in the library in hell, where he ended up after dying. EVERY SINGLE BOOK was word problems.

 

So count your blessings. Next time word problems are driving you nutzo, go to your library. Lots of other books available, right? At least we're not in hell! (Yet.  ;-)  )

 

Regards,

 

Eric Moline

McMinnville, OR