A coffee merchant combines coffee that costs 7 per pound...

Name: a coffee merchant combines coffee that costs 7 per pound with coffee that costs 410 per pound how many pounds of each should be used to make 29 lb of a blend costing 605 per pound 15436
Uploaded: 2020-03-28T01:19:54-08:00
Duration: 3 min 22 s
Channel: Julie Silva
Description: a coffee merchant combines coffee that costs 7 per pound with coffee that costs 410 per pound how many pounds of each should be used to make 29 lb of a blend costing 605 per pound 15436

A coffee merchant combines coffee that costs $7 per pound with coffee that costs $4.10 per pound. How many pounds of each should be used to make 29 lb of a blend costing $6.05 per pound?

Transcript

00:01 So in this problem, we're told that regular coffee is $4 per pound, and gourmet coffee costs $7 per pound.

00:08 Well, this shopkeeper is now going to try and get rid of 40 pounds of gourmet coffee, and what they're going to do is make a special blend.

00:15 The key here that isn't really stated explicitly in this problem is when they're talking about the gourmet blend, what they're blending is the regular coffee plus the gourmet coffee.

00:28 So that's something key to keep in mind.

00:31 They're going to mix those two to make a special mixture.

00:35 And this new gourmet blend is going to cost $5.

00:38 So what we're trying to figure out is how much of the regular coffee would we need in order for these two values to be equal.

00:47 So in other words, they want to know what would be equal if we were to take the original price for coffee per pound and the original cost of the gourmet per pound, and then how much regular coffee would we need in order for us to get rid of those 40 pounds of the gourmet coffee? so if i call regular coffee or the amount of regular coffee r, we know that 4 times r would be the total value in the amount of coffee that we earn for how much we sell.

01:18 And if we add to it 7g, where g is the amount of gourmet coffee that we sell, 7g would represent the amount that we would make for 7g.

01:27 Selling g pounds of gourmet coffee.

01:30 So 4r plus 7g would be the total amount earned to sell r pounds of regular coffee and g pounds of gourmet coffee.

01:39 Well, in this case, they're telling us that that should be equal to the same value as if we were to sell this gourmet blend.

01:47 Well, it's $5 for the gourmet blend per pound.

01:50 And remember, this gourmet blend is a mix of the regular coffee plus the gourmet coffee...

Question

A coffee merchant combines coffee that costs $7 per pound with coffee that costs $4.10 per pound. How many pounds of each should be used to make 29 lb of a blend costing $6.05 per pound?

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