SOLUTION: A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement? I came up with this

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Question 1207766: A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

I came up with this equation:
0.25x + 0.75x = 0.40(2x)
You say?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Fairly common two part mixture problem Sand is the filler. Concentration can emphasize the cement.

Maybe but often not necessary, try this:
                   FRACTION      AMOUNT        AMT. Only Cement

The Bag             0.25          20           0.25*20

Pure Cement        1.00           x          (1)(x)

TOTAL             9.40          x+20          x+(0.25)(20)

Equation to form should be obvious.

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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The 20-pound bag is 25% (=1/4) cement and 75% (=3/4) sand, so it contains 5 pounds of cement and 15 pounds of sand.

Let x be the number of pounds of cement you add. Then the number of pounds of cement is 5+x, and the total weight is 20+x.

You want the cement to be 40% of the total weight:

(5+x) = 0.40(20+x)

5+x = 8+0.40x
x-0.40x = 8-5
0.60x = 3
x = 3/0.60 = 5

ANSWER: 5 pounds

CHECK: the total weight is now 20+5 = 25 pounds; the number of pounds of cement is 5+5 = 10; 10/25 = 0.40
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

Your setup equation is  FATALLY  wrong.  It is irrelevant to wording description.
One item has no any relation to the other.
There is NO any logical connections between them.


This problem was solved at this forum many years ago  (perhaps,  15 years ago).

For solution,  see the link

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.512728.html#google_vignette



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