Lesson Word problems on mixtures for dry substances like candies, dried fruits

This Lesson (Word problems on mixtures for dry substances like candies, dried fruits) was created by by ikleyn(52754)

: View Source, Show
About ikleyn:

Word problems on mixtures for dry substances like candies, dried fruits

Problem 1

Ellen wishes to mix candy worth $1.90 per pound with candy worth $3.50 per pound to form 32 pounds of a mixture worth $2.80 per pound.
How many pounds of the more expensive candy should she use?

Solution

Let x be an amount of candies worth $1.90 per pound Ellen uses to mix, in pounds.
The amount of candies worth $3.50 per pound in the mix is 32-x pounds.

The total value of candies in the mix is 1.9x+3.5(32-x) dollars. At the price of the mix of $2.80 per pound it gives an equation

%281.9%2Ax+%2B+3.5%2A%2832-x%29%29%2F32

.

Simplify and solve it:

1.9*x + 3.5*(32-x) = 2.80*32.

1.9x + 112 - 3.5x = 89.6,

-1.6x = -22.4

x = 14.

32-14 = 18.

Answer. 14 pounds at $1.90 and 18 pounds at $3.50 should be used.

Problem 2

The Sweet Shoppe wishes to sell a mixture of chocolate covered pretzels & macadamia nuts. The pretzels worth $3 per pound and the nuts worth $8 per pound.
How many pounds of the nuts should be mixed with 50 pounds of the pretzels to make a mixture that would sell for $6 for pound?

Solution

Let x be an amount of nuts to mix in pounds.

Then the value of nuts is 8x dollars.

The value of pretzels is 3*50 dollars.

The balance equation is

Value of nuts + Value of pretzels = value of mixture, or

8x + 3*50 = 6(x+50).

Simplify and solve it:

8x + 150 = 6x + 300,

2x = 150,

x= 75.

Answer. 75 pounds of nuts should be added to the pretzels.

Problem 3

Joanne makes a mixture of dried fruits by mixing dried apples costing $6.00 per kilogram and dried apricots costing $8.00 per kilogram.
How many kilograms of each are needed to make 20 kilograms of a mixture worth $7.20 per kilogram?

Solution

Let x be an amount of dried apples to be mixed, in pounds.
Then the required amount of dried apricots is 20-x pounds.

The value of the dried apples is 6*x dollars; the value of the dried apricots is 8*(2-x) dollars.
The price of the mix should be $7.20. It gives an equation

%286x%2B8%2820-x%29%29%2F20

Simplify and solve it:

6x + 160 - 8x = 7.20*20,

-2x = -160 + 144,

-2x = -16,

x = 8.

20 - x = 20 - 8 = 12.

Answer. 8 kilograms of dried apples at $6 per kilogram and 12 kilograms of apricots at $8 should be mixed.

My other lessons on word problems for mixtures in this site are
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - Unusual word problem on mixtures
    - Check if you know the basics of mixtures from Science

    - Special type mixture problems on DILUTION adding water
    - Increasing concentration of an acid solution by adding pure acid
    - Increasing concentration of alcohol solution by adding pure alcohol
    - How many kilograms of sand must be added to a mixture of sand and cement
    - Draining-replacing mixture problems
    - How much water must be evaporated
    - Advanced problems on draining and replacing
    - Using effective methodology to solve many-steps dilution problems

    - Entertainment problems on mixtures

    - OVERVIEW of lessons on word problems for mixtures

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

This lesson has been accessed 5457 times.