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**+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

#1**+5 **

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**+5 **

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**+5 **

Melody, the first term in the third line of your derivation should be 0.2X not 0.23X.

.

Alan
Dec 2, 2014

#5**+5 **

Best Answer

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