6 Math
Name ______________________________
Unit 4: Proportional Reasoning
Problem Set 31: Ratio & Proportion Word Problems
Due Date ____________
1. A small university enrolls in-state and out-of-state students. The number of students enrolled in their
most recent freshman class was 243. The school reported that it enrolled 7 in-state students for every
2 out-of-state students. How many of each type of student were enrolled in the freshman class?
2. A junior high is interested in changing their student-to-worker ratio in the lunchroom in order to move
students through the line more quickly. During lunch, there are 45 students for every 2 workers. If there
are 215 more students than workers, how many students and workers are in the lunch room?
3. The varsity football team is full of juniors and seniors. At the beginning of summer training, there were
5 juniors to every 2 seniors. After several injuries and new players, the ratio was 4:3. If there are 48
juniors on the roster, how many seniors began the summer training?
4. Jenna and Becca were both selling cookies door to door. Jenna sold 8 boxes of cookies for every 3 boxes
of cookies Becca sold. Combined they sold a total of 385 boxes of cookies. How many boxes did each girl
sell?
5. At a local preschool there is a ratio of 3 boys to every 4 girls. If there are 245 total preschoolers enrolled,
how many are boys?
6. An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, the sold 147 more child
tickets than adult tickets. How many tickets did the amusement park sell on Saturday?
7. A paper store sells wrapping paper rolls and bags. In the spring, they order a ratio of 3:7 in wrapping
paper and bags. However, to prepare for the holiday season, they adjust the order and use a ratio of 5:5,
while still ordering the same total number of items. How many bags were ordered for the holiday season
if 150 rolls of wrapping paper were a part of their spring order?
8. Brock is training for a CrossFit competition. He began the training by completing pull-ups and box
jumps. Originally, his training plan had him completing pull-ups and box jumps at a ratio of 5:4. After
two months of training, he decided to focus on his leg strength and adjusted his ratio to 2:7. If he
completed 63 box jumps at the end of his training, how many pull-ups did he complete in the initial stage
of training?
9. An artist mixes yellow and blue paint to make the perfect shade of green. She uses 2 ounces of blue paint
for every 7 ounces of yellow paint.
(a) How many ounces of yellow paint will the artist need to add to 12 ounces of blue?
(b) The artist realizes she has 49 ounces of yellow left. How many blue ounces will she need to add?
(c) If the mixing container only holds 40 ounces of paint, what is the most green paint the artist can make
and what recipe should she use?
10. Folgers Coffee is priced at $12.88 for 80 cups of coffee and Seattle’s Best is priced at $9.00 for 50 cups.
Which brand of coffee is the better value for each cup?
11. The Olympic record for the 100m freestyle is 47.05 seconds for men. The Olympic record for the 50m
freestyle is 24.05 for women. Which record is the faster speed?
12. Ann can type 123 words in 3 minutes. Caroline can type 220 words in 5 minutes. Who can type the
faster speed?
13. Northside High School is having a spaghetti dinner fundraiser. In order to advertise, students place
flyers on neighborhood doors. Manaal hands out 120 flyers in 2 hours. Graciela hands out 18 flyers in
15 minutes. Who is able to pass out flyers at a faster rate?
Mr. Younts was restocking the shelves at Super Target when his tags got misplaced. Help him
match the correct item with the correct price tag.
(Show your work for these problems on a separate sheet of notebook paper and attach. You may write
your prices on the actual product once you’ve matched them).
Answers to Problem Set 31:
1.
There were 189 in-state and 54 out-of-state students enrolled in the freshman class.
2.
There are 10 workers and 225 students in the lunch room.
3.
24 seniors began the summer training.
4.
Jenna sold 280 boxes and Becca sold 105 boxes.
5.
There are 105 boys at the preschool.
6.
The amusement park sold 187 tickets on Saturday.
7.
There were 250 bags ordered for the holiday season.
8.
Brock complete 45 pull-ups in his initial stage of training.
9.
(a)
The artist will need 42 oz of yellow paint.
(b)
The artist will need to add 15 oz of blue paint.
(c)
The artist can make a maximum of 36 oz of green paint.
She should use 8 oz of blue paint and 28 oz of yellow paint.
10.
Folgers Coffee is the better value.
11.
The 100m Mens freestyle is the faster speed.
12.
Caroline can type at the faster speed.
13.
Graciela is able to pass out flyers at the faster rate.
Washing Powder: $7.80
Super Clean: $8.80
Salt: $3.60
Pepper: $6.72
Soda: $3.52
Popcorn: $9.00
Lemonade: $1.92