Partitive Proportions

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					                                     Partitive Proportions
 A partitive proportion of proportion by parts, describes a total amount
 being distributed into two or more unequal parts.

A nursery divides 360 acres of land into three sections to grow evergreen, flowering and fruit
trees in the ratio of 1:4:5. How many acres are used for each type?
                                            METHOD 1 – Use an equation

      1. Write an equation that relates the sum of the unequal parts to the whole.
                                         Let m = the number of acres in each part.

                         Evergreen       plus     flowering       plus     fruit   equals total acres

      2. Then find the number of acres in each unequal part.

                    METHOD 2 – Use separate proportions for each part-to-whole relationship.

      1. Find the sum of the parts given in the ratio – 1:4:5        1 + 4 + 5 = _____________.
      2. Write and solve separate proportions for each part-to-whole relationship.
         Define variables for each. Let a = evergreen trees, b = flowering trees, and c = fruit trees.

                  EVERGREEN                        FLOWERING                        FRUIT
   1. In an orchard of 1800 trees, there are peach, apple and pear trees planted in the ratio of
       7:3:2. How many trees of each kind are there?

   2. Tonya mixed paints in a ratio of 4 parts red to 5 parts blue. She used        gal of red paint.
      Find the total number of gallons of paint and the number of gallons of blue paint that
      she used.

   3. The perimeter of a triangle is 91 centimeters. If the sides are in the ratio 2 : 4 : 7, find
      the length of each side of the triangle.

   4. The perimeter of an irregular trapezoid is 46 meters. If the sides are in the ratio 2 : 3 : 5
      : 1.5, find the length of each sides of the trapezoid.

   5. Jack and Lea shared the driving during a trip across the country. For every 150 miles
      that Lea drove, Jack drove 200 miles. If the total driving distance was 2800 miles, how
      far did each person drive?
6. Suzanne owns a Farmville. For every 7 plots of soybeans she plants, she plants 10 plots
   of corn. She plants 1020 plots in all. How many plots of each crop does she plant?

7. Brandon and Marta are mowing a lawn. For every 4 square feet that Brandon mows,
   Marta mows 9 square feet. The lawn is 5200 square feet. How much lawn does each
   person mow?

8. Jeremy buys moving boxes for his dad’s company. His dad told him to buy a total of 288
   boxes and to buy 5 medium boxes for every 7 large boxes. How many of each size box
   should he buy?

9. Chef Kim plans to serve a fruit plate to each of 336 diners at a banquet. Each plate will
   contain 6 slices of kiwi, 3 pieces of mango, and 5 strawberries. How many pieces of
   each fruit are needed?

10.Three friends divided 156 baseball cards among themselves in a ratio of 4 : 1 : 6. How
   many cards did each receive?
11.A toy manufacturer made 1424 stuffed animals. They made teddy bears, bunnies and
   dogs in the ratio of 8 : 5 : 3. How many of each kind of stuffed animal did they make?

12.The main library purchased 938 new books. They want to distribute the new books to
   three of their branch libraries in ratio of 3 : 5 : 6. How many books will be given to each

13.A card store ordered 520 cards. They ordered birthday cards, anniversary cards and get
   well cards in the ratio of 6 : 3 : 1. How many of each card did they order?

14.At a nursery, there are 1248 flowers. There are roses, orchids, and carnations in the
   ratio of 3 : 4 : 6. How many of each kind of flower are there?

15.In a local election, 2640 votes were cast for two candidates. Mr. Wayne received 7
   votes for every 4 votes that Mr. Edwards received. How many votes did each candidate

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