Question

A market sells almonds for $2.00/lb and walnuts for $3.00/lb. The two types are mixed to create 65 pounds of nuts selling for $2.60/lb. How many pounds of each type of nut should be used in the mixture?

Answer 1

Number of pounds of almonds = 26
Number of pounds of walnuts = 39
26+39=65

Explanation:

Ah, now this following problem is solved through the use of simultaneous equations. You can read more about simultaneous equations here: http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/simultaneoushirev1.shtml

For now, however, let's just solve the equation.

So, to find how many pounds of walnuts and almonds are used in the mixture, lets say the number of pounds of almonds = `x` and the number of pounds of walnuts = `y`. Therefore, `x+y=65`

Then, `(65 times 2.6)` is the total amount of money that 65 pounds of the two combined amounts of nuts will equal. Thus, `2x+3y=169`

Now putting them together;

`x+y=65`
`2x+3y=169`

This will be solved using the "elimination method".

If we multiply the first equation by "2", then both equations will have a like term of " `2x`"

Thus,

`2x+2y=130`
`2x+3y=169`

Equation two is not altered in this case.

Now, we can remove the " `2x`" from both equations by subtracting them from each other. Therefore, we are left with:

`y=39`

Now, looking back, we defined `y` as being the number of pounds of walnuts per pound in the 65 pounds of mixed nuts. So, 39 pounds out of 65 pounds of the nuts are walnuts. Now, to find the number of almonds in the 65 kilos, we simply substitute in the `y` value into our original equation. Thus,

`x+39=65`

And therefore, `x=26`

Ultimately, the number of pounds of walnuts is equal to 39, and the number of pounds of almonds is equal to 26. Not confident with my working? Ok, we said that `2x+3y=169` right? If we substitute our newly found solutions for `x` and `y` into this equation, if it is correct, it should equal to 169.

So, `2(29) + 3(39) = 169`

Yay, it's right! Hope this helped, my friend :)

Answer 2

`39` lbs of walnut to be mixed with `26` lbs of almond.

Explanation:

Almond sells for `$2.0`/lb and walnut sells for `$3.0`/lb

Let `x` lbs of walnut is mixed with `(65-x)`lbs of almond to

get a mixture of `65` lbs for selling at `$2.60`/lb. By given

condition `3.0 x + 2.0(65-x) = 65 *2.60` or

`3x-2x=(65 *2.60) -2.0*65 or x = 65(2.6-2.0)` or

`x =65 *0.6=39` lbs `:. 65-x= 65-39=26` lbs . Hence

`39` lbs of walnut to be mixed with `26` lbs of almond. [Ans]