Question

Will you pinpoint the error in my work? Thanks.
See attachment

Answer 1

Let P = number of pounds of coffee at $20 per pound

Then,

20P + 90(60) = 50(60+P)
Crinkum – crankum here

2400 P = 30P
80 = P

Answer 2

(20P + (90)60 )/ 90 + P = 50

Answer 3

It seems like you had the right idea but you divided by 60 + x instead o f 90 + x. You're dividing by a weight, since the question asks you to find an answer in price/kg

Answer 4

i think it needs to be 20P +90(60) = 50(90+P) and not (60+P)

as you know that you'll have 90 pounds of one + P of the other

Answer 5

I set P = to the number of pounds but used it as a what? It's making me crazy. (crazier)

Answer 6

thats a good answer and breakin it down

Answer 7

Basically you're adding up prices on the left hand side of the equation, and you want to divide that price by a weight to get the price/weight of 50. However, you divided by 60 (a price) + P (a weight). It makes no sense to add these up, they don't represent the same quantities.

Answer 8

Somewhat like a mixed metaphor in grammar. Thanks. I'm going to reread all the replies when my head clears.

Answer 9

the right side of the equation should be $50 x the total amount of pounds used.
you know that the price is 50. you also know that there's 90 pounds used, and you need to know the x for the total amound of pounds.

20P + 90(60) = 50(90+P)

and not

20P + 90(60) = 50(60+P)

Answer 10

An easier way to make sure you get it right is to analyse what the question asks, however. You're asked to give an answer in the price/weight format, and you know that it has to equal 50$/pound.

50 =

You also know that you have two types of coffee, so you'll have to add up the price of these 2 types, as well as their weight. Since you know the answer has to be of the price/weight type, you know the numerator has to add up the total price, and the total weight goes to the denominator.

The total price will be (90*60) + (P*20). Now you have to ask yourself, are these values really giving you a price? Let's analyze the 90*60 part. 60 is a price per weight, which is [price]/[weight]. 90 is in kilograms, so it's a weight. That means 90*60 is actually:

\[[price]/[weight] * [weight] = [price]\]

As you can see, the units of the numbers act like variables, so they cancel out.

If you do the same work for the P*20 part of the equation, you'll end up with the same result.

At the denominator you know you need the total weight, since the answer has to be in a price/weight format. Here, you simply take 90 (the weight of the expensive coffee) + P (the weight of the less expensive coffee).

The right equation has been posted 2-3 times in this thread, but it really helps to break down the problem with this type of analysis. It might seem like a lot of work, but it's something that you do automatically when you get better. However, by analyzing the type of data you're working with, you can verify that you're giving an answer in the right format.

If you analyse the equation you posted, you'll notice that you were trying to add up a price with a weight, which makes no sense. That's a good indicator that you messed something up when you set up your equation.

Answer 11

Disregard this if it's confusing :P Dimensional analysis is usually brought up in physics classes by good teachers, it really helps when you understand the concept. Since physics can get confusing, it's a very good tool.

Answer 12

I am not confused by your explanation. I am now torqued out with myself that I did not see what was going on with my work. One of those - can't see the forest for the trees or is it can't see the trees for the forest? Thanks.

Answer 13

Glad I could help! Good luck to you :)

Answer 14

Arrange the pairs in the order: unit price * the pound:
$20 x + $60 * 90 = $50 ( x + 90 )
Then you won't be confused the price with the weight!

Answer 15

@Directrix It's just my lucky day, pls don't flatter me :")