MATH GENUISES!!! please help me!!!! my teacher doesnt teach me a thing!!!?

Question

How many pounds of coffee beans selling for $3.00 per pound should be mixed with 4 pounds of coffee beans selling for $1.40 per pound to obtain a mixture selling for $2.36 per pound?


please explain thoroughly and show your work!! :D i never learned this before. please say in a way so i can understand thanks!! and im in 8th grade so make it easy for me THANKS

Answer 1

You need to set up an equation with x = the number of pounds of $3.00 coffe beans you need.

The total price of the mixture will be:
3.00 * x + 1.40 * 4
= 3x + 5.60.

Now the weight of the mixture will be:
x + 4.

You want the price per pound to be $2.36, so your equation is
(total price of mixture) / (weight of mixture) = $2.36, or
(3x + 5.60) / (x + 4) = 2.36.

Solve for x (hint: cross-multiply). Good luck!

Answer 2

Ok, the strategy is this. First, assign variables. T is the lbs of $3 coffee and M is the lbs of the mixture selling for $2.36 per lbs. These are the two things you don't know.

Now you want to make an equation of the $. This is because you have price per lb and lbs. When you multiply these, you get $. So the equation is

$ for the 3$ coffee + $ for the $1.40 coffee = $ for the mixture.

T lbs * $3.00/lb + 4 lbs * $1.40/lb = M lbs * $2.36/lb

Each of these terms is lbs * $/lbs giving $.

But there are two variable, so you need a second equation. This is very easy becase T + 4 = M, the equation of the lbs of coffee. Now solve these equations simultaneously:

T*3 + 4 * 1.40 = M * 2.36
T + 4 = M
Substitution is easiet. Put T+4 in for M in the first equation.
T*3 + 5.6 = 2.36*(T+4)
.64*M + 5.6 = 9.44
T = (9.44 -5.6)/0.64
T = 6

T is the lbs of coffee at $3. So the total lbs of coffee is 6 + 4 = 10

Answer 3

If c = the number of pounds of coffee beans, than c+4 is the number of total pounds after you add the 4 lbs of cheaper beans.

So set up an equation using price times pounds:

3c + 1.40(4) = 2.36(4+c)

3c + 5.60 = 9.44 + 2.36c

Move the terms over and solve for c - you can do it from here? If not send an IM

Answer 4

Generally with mixture problems you need two equations. One expressing the quantities involved, and the other expressing the strenths or values involved. I see a fwe other people have shown you how to do it, and they did ok.
About the only thing I'd add is, when doing things like tihs, use variable names that represent what you're actually looking for. This way when you get to an answer you know what it means. Also using letters like x and y make it look harder than it is.
So your equations would look like this:
let e = the amount of coffee selling for 3.00 / lb (e for expensive)
and m = the amount of the resulting mixture.
Then your equation relating the amounts looks like this:
e + 4 = m
Next you need an equation relating the value of the mixture.
you have $3e worth of the expensive coffee
and (4x1.40) worth of the cheap coffee
and you want 2.36m worth of the mixture
So this eeuation looks like this:
3e + (4x1.40) = 2.36m
Now you have two equatios in two variables and where you go from here depends on what yo'uve learned about solving systems. If you've learned things like the addition method, also called the linear combinatio method, you'd use that. If you havn't you'd substitue the simpler equation into the more complicated one, as several other people have shown you.
Since e + 4 = m, substitute this on the right side.
3e + (4x1.40) = 2.36 (e+4)
Simplify
3e + 5.60 = 2.36e + (2.36x4) = 2.36e + 9.44
subtract 2.36 e from each side to get the e's all on one side
.64e + 5.60 = 9.44
subtract 5.60 to get the term with e by itself
.64e = 3.84
divide by .64 to get the e by itself
e = 6
so you need 6 lbs of the expensive coffee added to 4 lbs of the cheap coffee to make 10 lbs of the mixture.

Answer 5

This is a typical mixture problem.

x*3 +4(1.40) = (x+4)*2.36 There will be a total weight of (x+4) since you are trying to solve for the number of pounds "x" of the $3.00 bean.

Simplify this equation and obtain the answer.

Please spend more time on your math.. For an 8th grader, this should not be that difficult......

Answer 6

simple equation from the sentence X coffee beans @ $3.00/lb mixed (+) with 4 lbs of coffee @ $1.40 = a mixture of (4 lbs + X)@ $2.36/lb.

X(3) + 4(1.4) = (4 + X)2.36 Solve for X
X(3) + 4(1.4) = (4 x 2.36 )+ X2.36
X(3) - X(2.36) = (4 x 2.36 )-4 (1.4)
X (3-2.36) = 3.84
X=3.84/(3-2.36)= 6lbs of 3 $ coffee
put 6 in for X and it should satify each equation.

Answer 7

Let x pounds of coffee beans @$3.00 be mixed with 4 pounds of coffee beans to make x+4 pounds of coffee beans to be sold @$2.36 per pound
Cost of x pounds @$3=$3x
Cost of 4 " " $1.40=$5.60
Selling price of x+4 pounds @$2.36=2.36(x+4)=2.36x+9.44
By the problem ,the sum of the cost prices should be equal to the selling price
Therefore, 3x+5.60=2.36x+9.44
=>3x-2.36x=9.44-5.60
=>0.64x=3.84
=>x=3.84/0.64=6
Therefore,6 pounds of coffee beans selling for $3.00should be mixed
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Answer 8

You buy X pounds of coffee at $3 and 4 pounds at $1.40:
X pounds at $3 worth $3X
4 pounds at $1.40 worth $(4*1.40)

The resulting coffee weighs X+4 pounds, selling at $2.36:
X+4 pounds at $2.36 worth $(X+4)*2.36

The coffee you buy must be of equal value to the mixture selling at $2.36:

3*X+1.4*4 = (X+4)*2.36

Multiply out:
3X + 5.6 = 2.36X + 9.44

Gather all the terms with X to the left side and all the terms without to the right:

3X - 2.36X = 9.44 - 5.6

Simplify:
0.64X = 3.84

Divide to get X:
X = 6 pounds

Answer 9

Let x be the pounds of coffee beans.

Use the formula:
price = number of pounds x price per pound

Balance by the total price:
3x + 1.4(4) = (x+4)(2.36)

Solve for x,
x = 6 pounds

Answer 10

let x be the pounds needed
we have 3*x + 4*1.4 = (x+4) * 2.36 (after mixing we have x+4 pounds of the mixture)
=> x = 6 pounds