Question

Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 160 pounds of blended coffee beans selling for $3.75 per pound. She plans to do this by blending together a high quality bean costing $6.00 per pound and a cheaper bean at $2.00 per pound. To the nearest pound, find how much high quality coffee bean and how much cheaper bean she should blend

Answer 1

First you should identify your variables. Let's x be the quantity of cheap coffe and y quantity of expensive coffe. How much quantity of coffe (of both types) the problem says you need?

Answer 2

so i would do x and y first but how would i make an equation

Answer 3

Call the quantity of high-quality coffee is X
Cheaper coffee bean is Y
Since the total amount of coffee is 149 pound so
Have: X+Y= 149

Answer 4

Ok, the problem says you need 160 pounds of coffe, right?

Answer 5

Yeah, this is the first equation.

Answer 6

Well, but with 160 instead 149.

Answer 7

oh

Answer 8

So the total amount of coffe you need is,
\[x+y=160\] Ok?

Answer 9

okay

Answer 10

Well, now that you have the equation for the amount of coffe, you need the equation for the amount of money.

The total money for the cheap coffee is:
\[2\cdot x \]
The total money for the expensive coffee is
\[6\cdot y\]
The total money you will have is,
\[3.75\cdot160=600\] So the equation is,
\[2x+6y=600\]

Answer 11

Now you have your system of equations,
\[x+y=160\\
2x+6y=600\] Do you know how to solve it?

Answer 12

not really
i knowu have to get y alone right?

Answer 13

Yes, you can do it by substituion. In the first equation, solve for y you will get,
\[y=160-x\] Ok?

Answer 14

Now, plug this into the second equation, you will get,
\[2x+6(160-x)=600\]Ok? Now solve for x

Answer 15

You will get something like this,
\[2x+960-6x=600\Rightarrow -4x=-360\Rightarrow x=90\]

Answer 16

Now, with this value you can take whatever equation you want, plug in the value of x and obtain the value of y, for example, for the first equation
\[x+y=160\Rightarrow 90+y=160\Rightarrow y=70\]. And that is your solution
\[x=90, y=70\]

Answer 17

Do you understand it?

Answer 18

yes

Answer 19

Ok, perfect. Just if you need more problems like, remember that all of them solve the same way.