Problem 1 :
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Problem 2 :
A book has 50 more pages than nother book. If the total number of pages in both books is 400, how many pages does the larger book have?
Problem 3 :
If 15 is added to one-fourth of a number, the result is 4 times the number. What is the number?
Problem 4 :
If m + 6 is divided by 2 is 4 less than 4m, what is the value of m?
Problem 5 :
A hair shampoo comes in regular bottles and deluxe bottles. A deluxe bottle contains 6 more ounces of shampoo than a regular once. If four regular bottles and three deluxe bottles contain a total of 74 ounces of shampoo, how many ounces shampoo does a deluxe bottle contain?
Problem 6 :
Travelling a an average speed of 40 miles per hour, a bus takes 3 hours to complete its morning route. At what average speed, in miles per hour, must the bus travel if it is to complete its morning route in 2.5 hours?
Problem 7 :
Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers ?
Problem 8 :
If you subtract ½ from a number and multiply the result by ½, you get ⅛. What is the number?
Problem 9 :
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its width. What are the length and the width of the pool ?
Problem 10 :
The base of an isosceles triangle is ⁴⁄₃ cm. The perimeter of the triangle is 4²⁄₁₅ cm. What is the length of either of the remaining equal sides?
1. Answer :
Let x be one of the two numbers.
Then, the other number is (x + 15).
Given : Sum of two numbers is 95.
x + (x + 15) = 95
Simplify.
x + x + 15 = 95
2x + 15 = 95
Subtract 15 from each side.
2x = 80
Divider each side by 2.
x = 40
x + 15 = 40 + 15 = 55
The two numbers are 40 and 55.
2. Answer :
Let x be the number of pages in the smaller book.
Then, the number of pages in the larger book is (x + 50).
Given : Total number of pages in both books is 400.
x + (x + 50) = 400
x + x + 50 = 400
2x + 50 = 400
Subtract 50 from both sides.
2x = 350
Divide both sides by 2.
x = 175
x + 50 = 175 + 50 = 225
The larger book has 225 pages.
3. Answer :
Let x be the number.
Given : 15 is added to one-fourth of the number results times the number.
(¼)x + 15 = 4x
ˣ⁄₄ + 15 = 4x
Multiply both sides by 4.
4(ˣ⁄₄ + 15) = 4(4x)
4(ˣ⁄₄) + 4(15) = 16x
x + 60 = 16x
Subtract x from both sides.
60 = 15x
Divide both sides by 15.
4 = x
The number is 4.
4. Answer :
(m + 6) ÷ 2 = 4m - 4
⁽ᵐ ⁺ ⁶⁾⁄₂ = 4m - 4
Multiply both sides by 2.
2[⁽ᵐ ⁺ ⁶⁾⁄₂] = 2(4m - 4)
m + 6 = 8m - 8
Subtract m from both sides.
6 = 7m - 8
Add 8 to both sides.
14 = 7m
Divide both sides by 7.
2 = m
5. Answer :
Let the regular bottle contain x ounces shampoo.
Then, the deluxe bottle contains (x + 6) ounces.
Given : Four regular bottles and three delux bottles contain a total of 74 ounces of shampoo.
4x + 3(x + 6) = 74
4x + 3x + 18 = 74
7x + 18 = 74
Subtract 18 from both sides.
7x = 56
Divide both sides by 7.
x = 8
x + 6 = 8 + 6 = 14
A deluxe bottle contains 14 ounces shampoo.
6. Answer :
We know the following relaatiobship between speed, time and distance.
speed ⋅ time = distance ----(1)
Using the above relationship to find the morning route distance.
Substitute, speed = 40 and time = 3 in (1).
40 ⋅ 3 = Distance
120 = Distance
Morning route distance = 120 miles
Let x be the average speed to cover the morning distance 120 miles in 2.5 hours.
Substitute, speed = x, time = 2.5 and distance = 120 in (1) and solve for x.
x ⋅ 2.5 = 120
2.5x = 120
Divide both sides by 120.
x = 48
The bust must travel at an average speed of 48 miles per hour to complete its morning route in 2.5 hours.
7. Answer :
From the ratio 5 : 3, the two numbers can be assumed as
5x and 3x
Given : The two numbers differ by 18.
So, we have
5x - 3x = 18
2x = 18
Divide each side by 2.
2x/2 = 18/2
x = 9
5x = 5(9) = 45
3x = 3(9) = 27
Hence, the two numbers are 45 and 27.
8. Answer :
Let x be the required number.
From, the given information, we have
(x - ½) ⋅ ½ = ⅛
Multiply each side by 2.
(x - ½) ⋅ ½ ⋅ 2 = ⅛ ⋅ 2
(x - ½) ⋅ 1 = ¼
x - ½ = ¼
Add ½ to each side.
x = ¼ + ½
x = ¼ + ²⁄₄
x = ⁽¹ ⁺ ²⁾⁄₄
x = ¾
The required number is ¾.
9. Answer :
Let l be the length and w be the width of the swimming pool.
Given : Length is 2 m more than twice its width.
Then, the length is
l = 2w + 2
Given : The perimeter of the swimming pool is 154 m.
2l + 2w = 154
Substitute l = 2w + 2.
2(2w + 2) + 2w = 154
Simplify.
4w + 4 + 2w = 154
6w + 4 = 154
Subtract 4 from each side.
6w = 150
Divide each side by 6.
w = 25
Then, the length is
l = 2(25) + 2
l = 50 + 2
l = 52
The length and width of the rectangular swimming pool are 52 m and 25 m respectively.
10. Answer :
Let x be the length of each of the remaining two equal sides.
So, the sides of the triangle are
x, x and ⁴⁄₃
Given : The perimeter of the triangle is 4²⁄₁₅ cm cm.
x + x + ⁴⁄₃ = 4²⁄₁₅
2x + ⁴⁄₃ = ⁶²⁄₁₅
Subtract ⁴⁄₃ from each side.
2x = ⁶²⁄₁₅ - ⁴⁄₃
2x = ⁽⁶² ⁻ ²⁰⁾⁄₁₅
2x = ⁴²⁄₁₅
2x = ¹⁴⁄₅
Divide each side by 2.
2x = (¹⁴⁄₅) ÷ 2
x = (¹⁴⁄₅) x (½)
x = ⁷⁄₅
x = 1⅖
Length of either of the remaining equal sides is 1⅖ cm.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 01, 23 11:43 AM
Mar 31, 23 10:41 AM
Mar 31, 23 10:18 AM