**Problem 1 :**

A cookie factory uses 1/4 of a barrel of oatmeal in each batch of cookies. The factory used 1/2 of a barrel of oatmeal yesterday. How many batches of cookies did the factory make ?

**Solution :**

Amount of oatmeal used in each batch of cookies is

= 1/4 of a barrel

No. of cookies made yesterday is

= Oatmeal used yesterday / Oatmeal used in each batch

= (1/2) / (1/4)

= 1/2 ⋅ 4/1

= 2

So, the factory made 2 batches of cookies yesterday.

**Problem 2 :**

Of the students in the band, 1/4 play the flute and another 1/10 play the clarinet. What fraction of the students in the band play either the flute or the clarinet ?

**Solution :**

Fraction of the students in the band play either the flute or the clarinet is

= 1/4 + 1/10

LCM of (4, 10) is 20.

So, make each denominator as 20 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 2.

Then we have,

= (1 ⋅ 5) / (4 ⋅ 5) + (1 ⋅ 2) / (10 ⋅ 2)

= 5/20 + 2/20

= (5 + 2) / 20

= 7 / 20

So, the fraction of the students who play either the flute or the clarinet is 7/20.

**Problem 3 :**

Lily rode her bicycle 5/4 miles from her house to the park. Then she rode 3/2 miles from the park to the library. How many miles did Lily ride in all ?

**Solution :**

Total number of miles that Lily rode in all is

= 5/4 + 3/2

LCM of (4, 2) is 4.

So, make each denominator as 4 by multiplying the numerator and denominator of the first fraction by 1 and the second fraction by 2.

Then we have,

= (5 ⋅ 1) / (4 ⋅ 1) + (3 ⋅ 2) / (2 ⋅ 2)

= 5/4 + 6/4

= (5 + 6) / 20

= 11 / 4

= 2¾

So, Lily rode 2¾ miles in all.

**Problem 4 :**

At the dealership where Mary works, she fulfilled 1/6 of her quarterly sales goal in January and another 3/10 of her sales goal in February. If her quarterly sales goal is $12,000, what amount of sales did she make in January and February ?

**Solution :**

Fraction of her sales done in January and February is

= 1/6 + 3/10

LCM of (6, 10) is 30.

So, make each denominator as 30 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 3.

Then we have,

= (1 ⋅ 5) / (6 ⋅ 5) + (3 ⋅ 3) / (10 ⋅ 3)

= 5/30 + 9/30

= (5 + 9) / 30

= 14 / 30

= 7/15

Amount of sales she made in January and February is

= 7/15 of quarterly sales goal

= 7/15 ⋅ 12000

= 5600

So, amount of sales Mary made in January and February is $5,600.

**Problem 5 :**

Lucy made strawberry jam and raspberry jam. She made enough strawberry jam to fill 5/6 of a jar. If she made 2 times as much raspberry jam as strawberry jam, how many jars would the raspberry jam fill ?

**Solution :**

Amount of strawberry jam made by Lucy is

= 5/6 of a jar

2 times as much raspberry jam as strawberry jam is

= 2 ⋅ 5/6 of a jar

= 5/3 of a jar

= 1 ⅔ of a jar

So, Lucy would make enough raspberry jam to fill 1 ⅔ jars.

**Problem 6 :**

David's salary is $1800. David spent 2/3 of the total money for food. He spent 1/2 of the remaining for his kids education and saved the rest. How much did he save ?

**Solution :**

Money spent on food is

= 1800 ⋅ 2/3 = 1200

Remaining = 1800 - 1200 = 600 -------(1)

Money spent on kids education is

= 1/2 of remaining

= 1/2 ⋅ 600

= 300 --------(2)

Then, his savings is

= (1) - (2)

= 600 - 300

= 300

So, his savings is $300.

**Problem 7 :**

A, B and C are friends. A has 1/3 of money that B has. C has 1/2 of money that A has. If they all together have $450. How much money do A, B and C have separately ?

**Solution :**

Let us assume that B has the money "x".

Then, A = (1/3)x = x/3

C = 1/2 of A

C = 1/2 ⋅ x/3

C = x/6

**Given :** A + B + C = 300 -------> x/3 + x + x/6 = 450

4x/12 + 12x/12 + 2x/12 = 450

(4x+12x+2x)/12 = 450

18x/12 = 450

x = 300

So, we have

A = x/3 = 300/3 = 100

B = x = 300

C = x/6 = 300/6 = 50

So, A has $100, B has $450 and C has $50.

**Problem 8 :**

John's present age is 1/3 of David's age 5 years back.If David is 20 years old now, find the present age of John.

**Solution :**

Present age of David = 20 years

David's age 5 years back = 20 - 5 = 15 years

John's present age is 1/3 of David's age 5 years back

John's present age is

= 1/3 of 15 years

= (1/3) ⋅ 15

= 5 years.

So, John's present age is 5 years.

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