SOLUTION: A supermarket is selling 2 types of candies, orange slices and strawberry leaves. The orange slices cost $1.27 per pound and the strawberry leaves cost $1.77 per pound. How many po

Click here to see ALL problems on Equations

Question 1092935: A supermarket is selling 2 types of candies, orange slices and strawberry leaves. The orange slices cost $1.27 per pound and the strawberry leaves cost $1.77 per pound. How many pounds of each should be mixed to get a 13-pound mixture that sells for $19.01?

Found 3 solutions by josgarithmetic, greenestamps, josmiceli:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
x for the cheaper $1.27 per pound candy
y for the $1.77 per pound candy

Account for the mixture mass:

Account for the mixture COST:

More than one way to go from there. One of them is like this:

-

,

(NOTE: Misread problem; not saw the wrapped "1" at the end, on the page for the $19.01)

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

You want 13 pounds of candies. So

let x = pounds of orange slices, at $1.27 per pound
then 13-x = pounds of strawberry leaves, at $1.77 per pound

The total cost of the 13 pounds of candies is $19.01:

You need 8 pounds of orange slices and 13-8=5 pounds of strawberry slices.

Now here is a way to solve this kind of problem without using algebra and all those ugly decimals.

The cost of 13 pounds of strawberry leaves would be 13*1.77 = 23.01.
The cost of 13 pounds of orange leaves would be 13*1.27 = 16.51.
The actual cost of the 13 pounds of mixture is 19.01.

Where the 19.01 lies (think of it on a number line) between 16.51 and 23.01 exactly determines the ratio in which the two kinds of candies need to be mixed.

23.01-19.01 = 4.00;
19.01-16.51 = 2.50.

Those two differences tell us that the two candies need to be mixed in the ratio 4.00:2.50, or 8:5.

If there are 13 pounds of candies in the ratio 8:5, then there are 8 pounds of one and 5 pounds of the other.

Since the cost of the mixture is closer to 16.51 than it is to 23.01, the larger amount of candy must be the less expensive kind.

So you need 8 pounds of orange slices and 5 pounds of strawberry leaves.

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Let = pounds of orange slices
Let = pounds of strawberry leaves
------------------------------------------
(1)
(2)
------------------------------------------
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-------------------------------

and
(1)
(1)
---------------------
8 pounds of orange slices
5 pounds of strawberry leaves
--------------------------------
check:
(2)
(2)
(2)
(2)
OK