math ed stuff
"Solving Mixture Problems"
© Agnes Azzolino
1/8/2014, AMTNJ

Hand Out
What's Code?

      Code's a blend of words and mathematical symbols that takes the author from words to symbols in order to write or solve symbolic statements. CODE REWRITES ENGLISH AS ALGEBRA.

    It's not in the "Standards." last year

      Below, code is included in the algorithm.

  1. Double space the problem as needed.
  2. Underline the propositional phrases -- particularly those beginning with " of" -- so the info is not used in the topic sentence. (This may be omitted later.)
  3. Write the summarized TOPIC SENTENCE in words. THIS IS OFTEN THE "MEATIER" SENTENCE. (This may be omitted later.)
    Use no variables. Use only constants and words.
  4. Rewrite the topic sentence in code with
    ( multiplier)(item) encircled by parenthises.
  5. Below the topic code, rewrite the topic code using algebra and details from the propositional phrases or the original problem.
  6. Use complement/supplement/other number expressions as needed.
  7. Solve and check as usual.
    word problem with prepositional phrases underlined

		topic sentence summarized in words
		topic sentence summarized in code
		topic code with details in words and perhaps x
		topic code with algebra and x (equation)
		solved equation, answered question

      Please do problem 1.

Problem 1

	      Three consecutive integers are involved.  The 

	sum of the first, triple the middle, and four times

	the largest is 131.  Find the integers.

				(sum)				= 131
		 (first) + 3(middle) + 4(largest)	= 131
		 (x)     + 3(x + 1)  + 4(x + 2)	= 131
		   x     + 3x + 3   +   4x + 8	= 131
				      8x + 11	= 131
				      8x	= 120
				      x	= 15
			The numbers are 15, 16, 17.

Complement of an Angle, Supplement of an Angle, The Other Number

The Complement of an Angle
  • The complement of 40° is 50°.
  • The complement of 70° is 20°.
  • The complement of a number of degrees is (90 - x)°.

The Supplement of an Angle
  • The supplement of 40° is 140°.
  • The supplement of 70° is 110°.
  • The supplement of a number of degrees is (180 - x)°.

The Other Number
"The Rest"
  • The sum of two numbers is 12. One number is 10. The other number is 2.
  • The sum of two numbers is 12. One number is 3. The other number is 9.
  • The sum of two numbers is 12. One number is x. The other number is (12 - x). The "rest" is (12 - x).

Do Problem 5a

Do Problem 5b.

Stuff Problems
There are 12 toys in a box. Some are red. Some are green. They are worth $54. The red ones cost $6 each. The green ones cost $4 each. How many of each are there?
Red and blue toys worth $154 are in a bag. The red ones cost $12 each. The blue ones cost $5 each. There are 14 toys in all. How many of each kind are there?
Tickets for adults sell for $10, twice the price of the child's ticket. Twenty tickets are sold and raise $140. How many adult tickets are sold.
Ninety cents worth of ribbons are in a box containing blue and gold ribbons. The blue ribbons cost 5 cents each. The gold ribbons cost 10 cents each. The number of gold ribbons is 4 more than doubled the number of blue ribbons. How many gold ribbons are there?

Candy Problems

Red candies worth one dollar a pound and green candies
worth 4 dollars a pound are mixed to create $18 worth of candy.
There are two more pound of green candy than red candy.
Find how many pounds of each are mixed.
Some candy costing $1.85 per unit is mixed with some other
candy costing $2.45 per unit to make 24 units of $2 per unit candy. How much of the $2.45 candy is used?
Eight pounds of candy costing $3.50 per pound is a mixture
of $4/pound chocolate candy and $2/pound hard candy. If there is three times a much chocolate candy as hard candy, how many pounds of each are used?

Money Problems
A bank contains $2.10 in dimes and quarters. There are 7 more dimes than quarters. How many of each coin are there?
A bank contains 8 coins, an assortment of dimes, nickels, and quarters, which have a value of $ 1.00. There are twice as many dimes as quarters and all the rest of the coins are nickels. How many dimes, quarters, and nickels are in the bank?
A bank containing 15 coins in dimes, nickels, and quarters, has $1.70 in total. There are twice as many nickels as quarters. There is one more quarter than dime. How many nickels are there?

Do Problem 5c.

When double the complement of an angle is added to triple the supplement of the angle the result is 470 degrees. Find the measure of the angle.

Solution Problems
Some 70% punch is mixed with some 40% punch to produce 14 gallons of 53% punch. How many gallons of 70% punch are used?
She invested $6200. Some is invested at 12%. Some is invested at 8%. She earned a total of $728. How much was invested at 8%?

Consecutive Integers
  • Three consecutive integers are ____, _____, _______.
  • Three consecutive even integers are ____, _____, _______.
  • Three consecutive odd integers are ____, _____, _______.

Consecutive Integer Problems

The sum of three consecutive even integers is 12. Find the integers.
There are 3 consecutive even integers. The sum of triple
the first, double the second, and four times the third is 38. Find the integers.
There are 3 consecutive even integers. The sum of triple
the first, double the second, and four times the third is 56. Find the

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