WORD PROBLEMS ON COMPARING RATIOS

Problem 2 :

Jacob’s class had 8 boys and 10 girls. Olivia’s class had 9 boys and 15 girls. Which class has the greatest ratio of boys/girls?

Solution :

We should find ratio between boys to girls.

Jacob’s class :

= 8 : 10 (or) 8/10

Simplifying the fraction, we get

= 4/5 ----(1)

Olivia’s class :

= 9 : 15 (or) 9/15

Simplifying the fraction, we get

= 3/5 ----(2)

Comparing (1) and (2), we get

4/5 > 3/5

So, Jacob’s class has greater ratio.

Problem 3 :

For homework, Liam had 2 hours of math and 4 hours of science. Emma had 1 hour of math and 2 hours of science. Who had the greatest ratio of math/science homework?

Solution :

Ratio between math : science

Liam homework :

= 2 : 4 (or) 2/4

Simplifying the ratio, we get

= 1/2 ----(1)

Emma homework :

= 1 : 2 (or) 1/2 ----(2)

(1) and (2) are equal.

So, Liam and Hemma has equal ratios.

Problem 4 :

Ethan’s cookie recipe uses 3 cups of sugar to make 21 cookies. Mia’s recipe uses 4 cups of sugar to make 28 cookies. Which has a greater sugar/cookie ratio?

Solution :

Ratio between Sugar : Cookie

Ethan’s cookie recipe uses :

= 3 : 21

Simplifying the ratio, we get

= 1/7 ----(1)

Mia’s cookie recipe uses :

The ratio of Mia’s cookie recipe.

= 4 : 28 (or) 4/28

Simplifying the ratio, we get

= 1/7 ----(2)

(1) and (2) are equal.

So, Ethan’s and Mia’s has equal ratios.

Problem 5 :

Mason paid $54 for 9 lbs. of steak, and Isabella paid $72 for 6 lbs. which person paid a greater ratio of dollars/lbs. of steak?

Solution :

Mason paid :

The ratio of mason dollars to lbs. of steak ,

= 54 : 9 (or) 54 /9

= 6/1 ----(1)

Isabella paid :

= 72 : 6 (or) 72/6

= 12/1 ----(2)

By comparing (1) and (2), we get

So, Isabella has greatest ratio.

Problem 6 :

Michael’s class 27 adults and 63 kids on their field trip. Emily’s class had 20 adults and 70 kids on their trip. Whose class had a higher ratio of adults/kids on their trip?

Solution :

Michael’s class :

The ratio of Michael’s class adults : kids ,

= 27 : 63 (or) 27 /63

Doing simplification, we get

= 3/7 ----(1)

Emily’s class :

= 20 : 70 (or) 20 /70

= 2/7 ----(2)

Comparing (1) and (2)

= 3/7 > 2/7

So, Michael’s class has greater ratio.

Problem 7 :

Alex’s school had 20 buses for 400 students. Abbey’s school has 225 students riding 15 buses. Whose school has the greater ratio of students/buses?

Solution :

Alex’s school :

The ratio of Alex’s school : buses

= 20 : 400 (or) 20 /400

= 1/20 -----(1)

Abbey’s school:

= 15 : 225 (or) 15 /225

= 1/15  -----(2)

Comparing (1) and (2)

LCM (20, 115) is 60

= (1/20) ⋅ (3/3)

= 3/60

= (1/15) ⋅ (4/4)

= 4/60

= 4/60 > 3/60

So, Abbey’s has greatest ratio.

Problem 8 :

Jay had 5 candy bars and 20 pieces of gum in his Halloween bag. Madison had 9 candy bars and 12 pieces of gum. Who had the greater ratio of candy/ gum?

Solution :

Ratio between candy bars : pieces of gum

Jay :

= 5 : 20 (or) 5/20

By simplifying the fraction, we get

= 1/4  ----(1)

Madison :

= 9 : 12 (or) 9/12

= 3/4   ----(2)

By comparing (1) and (2), we get

= 3/4 > 1/4

So, Madison has greatest ratio

Problem 9 :

William’s team won 16 games and lost 4 games. Tracey’s team won 15 games and lost 5 games. Whose team had the greater ratio of wins/losses?

Solution :

Ratio between winning games : lost games

William’s team :

= 16 : 4 (or) 16/4

By simplifying the fraction, we get

= 4/1 ----(1)

Tracey’s team :

= 15 : 5 (or) 15/5

Dividing by 5 table, we get

= 3/1----(2)

Comparing (1) and (2), we get

4/1 > 3/1

So, William’s team has greatest ratio.

Problem 10 :

Steven walked 3 miles and drove 24 miles. Maureen walked 3 miles and drove 18 miles. Who has the greater ratio of miles walked/miles driven?

Solution :

Steven walked :

Distance covered by walk : by drive 

= 3 : 24 (or) 3/24

By simplifying using 3 times table, we get

= 1/8  ---(1)

Maureen walked :

= 3 : 18 (or) 3/18

= 1/6  ---(1)

By comparing (1) and (2), the denominators are not same. LCM (6, 8) is 24.

= 4/24 > 3/24

So, Maureen has greatest ratio.