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
= 1⅔ of a jar
So, Lucy would make enough raspberry jam to fill 1⅔ 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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