"Solving Mixture Problems"8 Agnes Azzolino1/8/2014, AMTNJ

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 parenthesis.

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

1. Three consecutive integers are involved. The sum of the first, triple the middle, and four times the largest is 131. Find the integers.

Complete.

A. The complement of a number of degrees is ____.

B. The supplement of a number of degrees is______.

C. The Other Number, "The Rest"

The sum of two numbers is 12. One number is x. The other number is ______.

5a. The sum of two numbers is 12. If the smaller number is doubled and added to the larger number, the result is 16. Find the numbers.

5b. An angle is three times the size of its complement. Find the angles.

6a. 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?

6b.* 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?

6c. 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.

6d.* 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?

8a. 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.

8b. 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?

8c. 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?

9a.* A bank contains $2.10 in dimes and quarters. There are 7 more dimes than quarters. How many of each coin are there?

9b.* 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?

9c. 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?

5c. There are 12 coins in a bank and the coins have a value of $1.20. There are five more dimes than nickels and all the rest of the coins are quarters. Find how many dimes are in the bank.

10. 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.

11a. Some 70% punch is mixed with some 40% punch to produce 14 gallons of 53% punch. How many gallons of 70% punch are used?

11b.* 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%?

Complete:

Three consecutive integers are

____, _____, ______.

Three consecutive even integers are

__, ____, _____.

Three consecutive odd integers are

___, _____, _____.

7a. The sum of three consecutive even integers is 12. Find the integers.

7b. 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.

7c. There are 3 consecutive even integers. The sum of triple the first, double the second, and four times the third is 56. Find the integers.