Problem 1 :
$5000 is donated to a poor family. In the family, there are seven members - father, mother, and five children. Father and mother together took half of the money and the rest is shared equally among the five children. Find the share of each child.
Problem 2 :
Divide a positive number by 5 and add 4 to it. Further multiply it by 3 and subtract 7 from the result. If the final answer is 44, find the positive number.
Problem 3 :
An amount of money is divided into three equal parts. Later, the first part is divided equally among five children and each child receives $60, find the original amount of money.
Problem 4 :
$1800 is divided into three equal parts. Later, the first part is divided equally among five children, the second part is divided equally among four brothers and the third part is divided equally among three sisters. If each child receives $x, each brother receives $y and each sister receives $z, find the values of x, y and z.
Problem 5 :
A box of pencils costs $3 and each box contains 4 pencils. A box of pens costs $7.50 and each box contains 5 pens. Find the total cost of 3 pencils and 10 pens.
Problem 6 :
John had $50 and borrowed $200 from his friend. He bought 2 shirts for $20 each, a pair of trousers for $32 and 3 pairs of shoes for $28 each. After having spent money for the above items, How much did he have left?
1. Answer :
The share of each child :
= (5000/2) ÷ 5
= 2500 ÷ 5
= $500
2. Answer :
Let x be the required positive number.
3[(x ÷ 5) + 4] - 7 = 44
Add 7 to both sides.
3[(x ÷ 5) + 4] = 51
Divide both sides by 3.
(x ÷ 5) + 4 = 17
Subtract 4 from both sides.
x ÷ 5 = 13
x/5 = 13
Multiply both sides by 5.
x = 65
The positive number is 65.
3. Answer :
Let x be the original amount of money.
Since the original amount of money is divided into three equal parts, then each part is
= x/3
Given : The first part is divided equally among five children and each child receives $60.
(x/3) ÷ 5 = 60
x/15 = 60
Multiply both sides by 15.
x = 900
The original amount of money is $900.
4. Answer :
$1800 is divided into three equal parts.
Then, the value of each part is
= 1800/3
= 600
Given : The first part is divided equally among five children and each child receives $x.
x = 600/5
x = 120
Given : The second part is divided equally among four brothers and each brother receives $y.
y = 600/4
y = 150
Given : The third part is divided equally among three sisters and each sister receives $z.
z = 600/3
z = 200
5. Answer :
Given : A box with 4 pencils costs $3.
Cost of 4 pencils = $3
Cost of 1 pencil = 3/4
= $0.75
Given : A box with 5 pencils costs $7.50.
Cost of 5 pens = $7.50
Cost of 1 pen = 7.50/5
= $1.50
The total cost of 3 pencils and 10 pens :
= 3(0.75) + 10(1.50)
= 2.25 + 15
= $17.25
6. Answer :
The total amount of money that John had :
= 50 + 200
- $250
The total amount of money that John spent for purchase :
= 2x20 + 32 + 3x28
= 40 + 32 + 84
= $156
Amount of money John had left after purchase :
= 250 - 156
= $94
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