Problem

A photographer wishes to mix 2 liters of a $5 \%$…

04:36

Problem 77 Hard Difficulty

A store sells regular coffee for $\$ 4$ a pound and gourmet coffee for $\$ 7$ a pound. To get rid of 40 pounds of the gourmet coffee, the shopkeeper plans to make a gourmet blend that he will put on sale for $\$ 5$ a pound. How many pounds of regular coffee should be used?

Answer

80 lb of regular coffee

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 8

An Introduction to Functions

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Video Transcript

So in this problem, we're told that regular coffee is $4 per pound and gourmet coffee costs $7 per pound. Well, this shopkeeper is now going to try and get rid of £40 of gourmet coffee, and what they're going to do is make a special blend. The key here that isn't really ah stated explicitly in this problem is when they're talking about the gourmet blood, what they're blending is the regular coffee, plus the gourmet coffee. So that's something he the keep in mind. They're gonna mix those two to make a sex special mixture, and this new gourmet blend is going to cost $5. So what we're trying to figure out is how much off the regular coffee would we need in order for these two values to be equal? So in other words, they want to know why what would be equal if we were to take the original price for coffee per pound and the original original cost of the gourmet per pound. And then how much regular coffee would we need in order for it? For us to get rid of those £40 of the gourmet coffee. So if I call regular coffee or the amount of regular coffee are we know that four times are would be the total value in the amount of coffee that we earn for how much we sell and if we add to it. Seven. G Where G is the amount of gourmet coffee that we sell, seven G would represent the amount that we would make for selling G pounds of gourmet coffee. So for our plus seven, G would be the total amount earned to sell our pounds of regular coffee and G pounds a gourmet coffee. Well, in this case, they're telling us that that should be equal to the same value as if we were the cell. This gourmet blood? Well, it's $5 for the gourmet blend per pound. And remember, this gourmet blend is a mix of the regular coffee plus the gourmet coffee. So this is our equation right here? Well, they tell us that we're trying to get rid of £40 of the gourmet coffee, so that tells us that G is equal to 50. So we're going to substitute for the in Fergie. So we're gonna have four are plus seven times 40 and that's going to equal to five times are plus 40. And now we simply need to solve this equation. While on the left hand side of the equation, we have seven times 40 which is to 80. So we'll have four R plus 2 80 equals. Well, on the right hand side, we need to distribute. The five to both terms in the preface is, well, five times are is five r and five times 40 is 200. Now. To solve this equation, I can subtract. Four are to both sides of the equation because four are minus four. R is zero, so those would cancel. So I'm left with 2 80 is equal to our plus 200. And now I simply need to subtract 200 from both sides of the equation and to a T minus 200 is equal to a T equals are. So what we found is that they would need to sell £80 of regular coffee

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