I need help with a tough math word problem...?

Question

At the local IGA grocery store, the manager mixed nuts worth $4.00 per pound with raisins worth $3.25 per pound to make a 15 pound mixture of trail mix to be sold for $3.60 per pound. How many pounds of nuts were used in the mixture?

Answer 1

Not enough information is given. The answer reached by all the others is silently assuming that the manager is happy to make no extra profit from selling the mixture, compared to selling its separate components.

If I was the manager, I would put in maybe 5 pounds of nuts and 10 of raisins, to get some extra profit for the work of making up the mixture and repackaging it.

Answer 2

The total mixture weighs 15 pounds and costs $54 because every pound costs $3.60 per pound and there are 15 pounds ($3.60 x 15).
Since there are 15 pounds in the mixture, there must be (15 - X) + X pounds of mixed nuts and raisins respectively in the mixture.
Thus let (15 - X) represent the number of pounds for mixed nuts and X represent the number of pounds for raisins. The cost then of the mixed nuts would be ($4.00 x (15 - X)) while the cost of the raisins would be ($3.25 x X). We add these two costs and equate that with the cost of the mixture ($3.60 x 15).
Thus we have:
4(15 - X) + 3.25X = 3.60 x 15
60 - 4X + 3.25X = 54
60 - 54 = 4X - 3.25X
6 = .75X
6/.75 = X
8 = X
X = 8
Thus we have 8 pounds of raisins and 7 pounds of mixed nuts in the mixture.

Answer 3

First, let's look at how much of each product were in the mixture.

We have 15 total, so, abritrarily choosing:
Let's say nuts have [x] lbs and raisins have the rest, or 15-[x] lbs.

The equation we need to set up to determine the final cost of the mix is:

(# of nuts)(unit cost of nuts) + (# of raisins)(unit cost of raisins) = (# of mix)(unit cost of mix)

Now, let's plug in the values:
([x] lb)($ 4 / lb) + (15-[x] lb) ($3.25 / lb) = (15 lb)($3.60 / lb)
or
4x + 15*3.25 - 3.25x = 54

(4-3.25) x = 54-15*3.25
0.75 x = 54 - 48.75 = 5.25

x = 5.25 / 0.75 = 7 lbs.

Checking: 4*7 + 3.25*8 = 28 + 26 = 54

Answer 4

let the pounds of nuts be denoted as x
& the pounds of raisins be y

x + y = 15 .....(1)

4x + 3.25y = 3.6(x + y)

4x + 3.25y = 3.6*15

4x + 3.25y = 54... (2)

Solving 1 & 2 simultaneously we get,

4x + 4y = 60
4x + 3.25y = 54

0.75y = 6

y = 8 pounds of raisins

x = 7 pounds of nuts.

Answer 5

total sale prive=15*3.60=$54
let x=# of nuts
4x+3.25(15-x)=54
4x-3.25x+48.75=54
.75x=54-48.75=5.25
x=5.25/.75=7 # of nuts
check
7# nuts @$4/#=$28
8#raisins @ $3.25=$26
$26+$28=$54
$54/$3.6/#=15#

Answer 6

Let "n" be a pound of nuts and "r" be a pound of raisins:

n + r = 15
r = 15 - n

4n + 3.25r = 15 * 3.60

4n + (3.25 * (15 - n)) = 54
4n + 48.75 - 3.25n = 54
.75n = 5.25
n = 7
r = 8

Answer 7

enable the quantity of 30% be x, then something is 20-x of the 70% 30 x + (20-x) 70 = 20(50) -40x + 1400 = one thousand x = 10 of the 30% 20-x = 10 of the 70% because 50% is halfway between 30% and 70%, this makes suitable experience !

Answer 8

let x pound be nuts and y pound be raisins

then 4x +3.25y = 3.6 * 15........................ (1)
x + y = 15 .......................... (2)

solving,
x = 7
and y =8
therefore answer is 7 pound nuts

Answer 9

Whoa Im getting sleepy ! the real confusion here is probably the way its worded.

Answer 10

confused