Lesson Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts

Source code of 'Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts'

This Lesson (Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts) was created by by ikleyn(52756)

: View Source, Show
About ikleyn:

<H2>Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts</H2>

<H3>Problem 1</H3>A coffee shop has coffee which worth &nbsp;$6&nbsp; per pound. &nbsp;They want to mix it with &nbsp;20&nbsp; pounds of coffee which worth &nbsp;$9&nbsp; per pound to get 
a mixture that can be sold for &nbsp;$8&nbsp; per pound. How many pounds of the cheaper coffee should they use?

<B>Solution</B>

Let &nbsp;<B>x</B>&nbsp; be the number of pounds of coffee worth &nbsp;$6&nbsp; per pound what should be mixed. &nbsp;It costs &nbsp;6*x &nbsp;dollars.

20 pounds of &nbsp;$9&nbsp; coffee costs &nbsp;9*20&nbsp; dollars. &nbsp;In total, &nbsp;the mix costs &nbsp;6x + 9*20 &nbsp;dollars.

Hence, &nbsp;one pound of the mix costs &nbsp;{{{(6x + 9*20)/(x+20)}}}.  &nbsp;Thus you have an equation to determine &nbsp;<B>x</B>

{{{(6x + 9*20)/(x+20)}}} = {{{7}}}.

Simplify and solve it:

6x + 180 = 7*(x+20), &nbsp;&nbsp;&nbsp;&nbsp;(after multiplying both sides by (x+20) )

6x + 180 = 7x + 140,

180 - 140 = 7x - 6x,

40 = x.

<B>Answer</B>. &nbsp;x = 40. &nbsp;&nbsp;40 &nbsp;pounds of the &nbsp;$6 &nbsp;coffee should be mixed with &nbsp;20 &nbsp;pounds of &nbsp;$9 &nbsp;coffee to get the mix at the price of &nbsp;$7 &nbsp;per pound.

<H3>Problem 2</H3>Chocolate coffee beans sell for &nbsp;$7.00&nbsp; per pound and hazelnut coffee beans sell for &nbsp;$6.10&nbsp; per pound. &nbsp;One customer wants 
a 6 pound mixture of both types of coffee. &nbsp;How many pounds of each should be used if the mixture is to cost &nbsp;$6.40&nbsp; per pound?

<B>Solution</B>

Let &nbsp;c&nbsp; be the number of pounds of the chocolate coffee and &nbsp;h&nbsp; be the number of pounds of the hazelnut coffee to be mixed.

So, &nbsp;your first equation is:

c + h = 6

The cost of the mix should be &nbsp;6*$6.40 = $38.40. &nbsp;From the other side, &nbsp;it is 7*c + 6.10*h. &nbsp;Thus you have the second equation

7*c + 6.10*h = 38.4.

Now, &nbsp;you can solve this system of two equations by substitution.

c = 6 - h,

7(6-h) + 6.1h = 38.4,

42 - 7h + 6.1h = 38.4,

42 - 0.9h = 38.4,

-0.9h = -3.6,

h = 4.

c + 4 = 6.

c = 2.

<B>Answer</B>. &nbsp;2&nbsp; pounds of chocolate coffee and &nbsp;4&nbsp; pounds of hazelnut coffee should be used.

<H3>Problem 3</H3>A customer has asked a caterer for &nbsp;60 LB of nuts, &nbsp;60% of which are to be cashews. 
The caterer has available mixtures of &nbsp;70% cashews and &nbsp;45% cashews. &nbsp;How many pounds of each mixture should be used?

<B>Solution</B>

The caterer needs to mix &nbsp;<B>x</B>&nbsp; lbs of the &nbsp;70% cashew mixture with &nbsp;(60-<B>x</B>)&nbsp; lbs of the &nbsp;45% cashew mixture to obtain the &nbsp;60 lbs of &nbsp;60% cashew mixture.

Change the percentages to their decimal equivalents and write the algebraic equation to solve for &nbsp;<B>x</B>.

0.7*x + 0.45*(60-x) = 0.6*60.

Simplify and solve for &nbsp;<B>x</B>.

0.7x + 27 - 0.45x = 36.

Combine like-terms.

0.25x = 36-27,

0.25x = 9.

Divide both sides by &nbsp;0.25.

x = 36.

<B>Answer</B>. &nbsp;The caterer should mix &nbsp;36 lbs of the &nbsp;70% cashew mixture with &nbsp;(60-36 = 24) lbs of the &nbsp;45% cashew mixture to obtain &nbsp;60 lbs of &nbsp;60% cashew mixture.

<H3>Problem 4</H3>Peanuts sell for &nbsp;$3.00 &nbsp;per pound. &nbsp;Cashews sell for &nbsp;$6.00 &nbsp;per pound.  &nbsp;How many pounds of cashews should be mixed 
with &nbsp;12 &nbsp;pounds of peanuts to obtain a mixture that sells for &nbsp;$4.20 &nbsp;per pound?

<B>Solution</B>

Let &nbsp;x&nbsp; be the number of pounds of cashews to be mixed.

So, &nbsp;the weight of the mix is &nbsp;12 + x &nbsp;pounds.

The cost of the mix should be &nbsp;12*$4.20 = $50.40. &nbsp;From the other side, &nbsp;it is 12*3 + 6.00*x &nbsp;dollars. &nbsp;Thus you have an equation

12*3 + 6.00*x = 50.40.

Simplify and solve the equation:

6x =50.40 - 36,

6x = 14.40,

x = {{{14.40/6}}} = 2.4.

<B>Answer</B>. &nbsp;2.4&nbsp; pounds of cashews should be used.

My other lessons on word problems for mixtures in this site are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-antifreeze-solutions.lesson>Word problems on mixtures for antifreeze solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-cookies-candies.lesson>Word problems on mixtures for dry substances like candies, dried fruits</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-soil-and-sand.lesson>Word problems on mixtures for dry substances like soil and sand</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-alloys.lesson>Word problems on mixtures for alloys</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problems.lesson>Advanced mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-mixture-problem-for-three-alloys.lesson>Advanced mixture problem for three alloys</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Unusual-word-problem-on-mixtures.lesson>Unusual word problem on mixtures</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Check-if-you-know-the-basics-of-mixtures-from-Science.lesson>Check if you know the basics of mixtures from Science</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Special-type-mixture-problems-on-DILUTION-adding-water.lesson>Special type mixture problems on DILUTION adding water</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Increasing-concentration-of-an-acid-solution-by-adding-pure-acid.lesson>Increasing concentration of an acid solution by adding pure acid</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Increasing-concentration-of-alcohol-in-solution-by-adding-pure-alcohol.lesson>Increasing concentration of alcohol solution by adding pure alcohol</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/How-many-kilograms-of-sand-must-be-added-to-a-mixture-of-sand-and-cement.lesson>How many kilograms of sand must be added to a mixture of sand and cement</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Draining-replacing-mixture-problems.lesson>Draining-replacing mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/How-much-water-should-be-evaporated.lesson>How much water must be evaporated</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Advanced-problems-on-draining-and-replacing.lesson>Advanced problems on draining and replacing</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Using-effective-methodology-to-solve-many-steps-dilution-problems.lesson>Using effective methodology to solve many-steps dilution problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Entertainment-problems-on-mixtures.lesson>Entertainment problems on mixtures</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/OVERVIEW-of-lesson-on-word-problems-for-mixtures.lesson>OVERVIEW of lessons on word problems for mixtures</A>

Use this file/link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>&nbsp; to navigate over all topics and lessons of the online textbook &nbsp;ALGEBRA-I.