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# Mrs. Alderidge operates a soybean farm outside of Grinnell, Iowa. To keep costs down, she buys many products in bulk and transfers them to s

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Mrs. Alderidge operates a soybean farm outside of Grinnell, Iowa. To keep costs down, she buys many products in bulk and transfers them to smaller containers for use on the farm. Often the bulk products are not the correct concentration and need to be custom mixed before Mrs. Alderidge can use them. One day she wants to apply fertilizer to a large field. A solution of 63% fertilizer is to be mixed with a solution of 43% fertilizer to form 40 liters of a 53% solution. How much of the 63% solution must she use?

 a. 20 L b. 34 L c. 15 L d. 32 L
mishforever21  Dec 1, 2014

#5
+80922
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Here's another way to do this with only one variable.

Call the amount of the 63% solution = "x"...then the amount of the 43% solution is just "40-x"..we have

.63x + .43(40-x)  = .53(40)     multiply through by 100

63x + 43(40-x) = 53(40)

63x + 1720 - 43x = 2120      simplify

20x  = 400       divide through by 20

x= 20 L

CPhill  Dec 4, 2014
Sort:

#1
+91436
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Let X be the amount of 63% soln used and let Y be the amount of 43% solution used.

$$\begin{array}{rlll} X+Y&=&40\qquad \qquad & (1)\\ 0.63X+0.43Y&=&0.53(X+Y)& (2)\\ 0.20X+(0.43X+0.43Y)&=&0.53*40\qquad Error fixed - thanks Alan\\ 0.20X+0.43(X+Y)&=&21.2\\ 0.20X+0.43*40&=&21.2\\ 0.20X+17.2&=&21.2\\ 0.20X&=&4\\ X&=&4/0.20\\ X&=&20\\ \end{array}$$

so it seems that 20L of the 63% solution was needed.

Melody  Dec 2, 2014
#2
+91436
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Maybe you were supposed to ESTIMATE the answer

A solution of 63% fertilizer is to be mixed with a solution of 43% fertilizer to form 40 liters of a 53% solution. How much of the 63% solution must she use?

Choices     20L, 34L, 15L, 32L

The 63% solution is too strong by 10% and the 43% is too week by 10% so if i had to guess I would say 50% of each is needed.  That is 20L each.

Again: This answer has  been edited.

Melody  Dec 2, 2014
#3
+26399
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Melody, the first term in the third line of your derivation should be 0.2X not 0.23X.

.

Alan  Dec 2, 2014
#4
+91436
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Thanks Alan,

Much appreciated :)

Melody  Dec 3, 2014
#5
+80922
+5

Here's another way to do this with only one variable.

Call the amount of the 63% solution = "x"...then the amount of the 43% solution is just "40-x"..we have

.63x + .43(40-x)  = .53(40)     multiply through by 100

63x + 43(40-x) = 53(40)

63x + 1720 - 43x = 2120      simplify

20x  = 400       divide through by 20

x= 20 L

CPhill  Dec 4, 2014

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