PROBLESM ON RATIO AND RATES

Problem 1 :

The ratio between the number of Anita's cousins and the number of Juan's cousins is 5:8. If Anita has 15 cousins, how many does Juan have?

A) 5       B) 8      C) 24     D) 40

Solution :

Anita's cousins : Juan's cousins = 5 : 8

Number of Anita's cousins = 5x

Number of Juan's cousins = 8x

5x = 15

Dividing by 5, we get

x = 3

Number of Juan's cousins = 8(3) ==>  24

So, there are 24 cousins for Juan.

Problem 2 :

Allison sells apples at the market. On a given day, the ratio of red delicious to Macintoshes to granny smiths sold is 4:3:2. If her truck can carry 180 bushels of apples, how many bushels of granny smiths should she include? 

A) 90          B) 80           C) 60            D) 40

Solution :

Number of red delicious = 4x

Number of Macintoshes = 3x

Number of granny smiths = 2x

Number of apples that container can hold = 180

4x + 3x + 2x = 180

9x = 180

Dividing by 9, we get

x = 180/9

x = 20

Number of bushels of granny smith = 2(20)

= 40

Problem 3 :

The cost of a luxury car compared to a mid-size family car is in the ratio 3:2. The cost of the mid-size family car to an economy car is 2:1. What is the ratio between the cost of a luxury car and the cost of an economy car?

A)  2:1    B) 3:1    C) 5:1      D) 6:1

Solution :

Ratio between luxury car : mid size family car = 3 : 2

Ratio between mid size family car : economy car = 2 : 1

3 : 2 = 2 : 1

Ratio between luxury car : economy car = 3 : 1.

Problem 4 :

If the Banded Peak school bus travels 2531 km in 26 hours, what unit rate correctly identifies their speed? 

A) 97.3km/h   B) 2531km/26 h   C) 97 km/h   D) 98 km/h

Solution :

Unit rate = 2531 / 26

Problem 5 :

It costs $3.99 for 25 fl.oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?

Solution :

By finding the unit rate, we can decide which is the better buy.

Cost of 25 fl.oz of detergent = $3.99

Cost of 1fl.oz of detergent = 3.99/25

= 0.159

Cost of 90 fl.oz of detergent = $6.99

Cost of 1fl.oz of detergent = 6.99/90

= 0.077

So, $6.99 for 90 fl. oz is the better choice.

Problem 6 :

A 16 oz package of brown rice costs 79 cents and 32 oz package of white rice costs $3.49. Which package is a better deal?

Solution :

Cost of 16 oz package = 0.79

Cost of 1oz package = 0.79/16 ==> 0.0493

Cost of 32 oz package = 3.49

Cost of 1oz package = 3.49/32 ==> 0.1090

So, 16 oz package is the better deal.

Problem 7 :

A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second?

Solution :

Distance covered by the sky diver in 3 seconds = 144

Distance covered 1 second = 144/3

= 48

So, he can cover 48 feet in 1 second.

Problem 8 :

The greatest ratio among the ratios 2 : 3, 5 : 8 and 40 : 25 is

A) 2 : 3     B) 5 : 8     C) 40 : 25     D) all are equal

Solution :

Writing the given ratios as fractions, we get

2/3, 5/8 and 40/25

Simplifying 40/25, we get 8/5

Now to compare three fractions 2/3, 5/8 and 8/5, we have to make the denominators same.

LCM (3, 8, 5) is 120

(2/3) ⋅(40/40) = 80/120

 (5/8) ⋅(15/15) = 75/120

(8/5) ⋅(24/24) = 192/120

8/5 is greater of all. So, 40 : 25 is the greater ratio.

Problem 9 :

A pump moves 42 gallons in seven minutes. Find the unit rate.

Solution :

Unit rate = 42/7

So, the required unit rate is 6 gallons.

Problem10 :

You score 84 points in six games. How much do you score per game?

Solution :

Points scored in six games = 84

Points scored in one game = 84/6

= 16 points.