This document provides 15 examples of word problems involving numbers. Each example presents a multi-step word problem, shows the steps to define variables, write equations, and solve for the unknown values. The examples cover a range of problem types including finding missing numbers based on relationships between amounts, averages, sums, differences, products, and ratios.
In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
Directions Please show all of your work for each problem. If app.docxduketjoy27252
Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. The option of hand writing your work and scanning it is acceptable.
1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 5
22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
23. Identify the property that is illustrated by the following statement.
10 (3 + 11) = 10 3 + 10 11
24. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)
25. Add. 14 + (–6)
26. Subtract. –17 – 6
27. Evaluate. 3 – (–3) – 13 – (–5)
28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
31. Evaluate. (–9)(0) + 13
32. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?
33. Write the following phrase using symbols: 2 times the sum of v and p
34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 4
35. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?
36. Write the following geometric expression using the given symbols.
times the Area of the base (A) times the height(h)
37. Evaluate if x = 12, y = , and z = .
38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
39. If the circumference of a circle whose radius is r is given by C = 2πr, in which π ≈ 3.14, find the circumference when r = 15 meters (m).
40. Combine like terms: 9v + 6w + 4v
41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.
42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.
43. Use the distributive property to remove the p.
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
1. Free GK Alerts- JOIN OnlineGK to 9870807070
7. PROBLEMS ON NUMBERS
In this section, questions involving a set of numbers are put in the form of a puzzle. You have to
analyze the given conditions, assume the unknown numbers and form equations accordingly,
which on solving yield the unknown numbers.
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SOLVED EXAMPLES
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Ex.1. A number is as much greater than 36 as is less than 86. Find the number.
Sol. Let the number be x. Then, x - 36 = 86 - x => 2x = 86 + 36 = 122 => x = 61.
Hence, the required number is 61.
Ex. 2. Find a number such that when 15 is subtracted from 7 times the number, the
Result is 10 more than twice the number. (Hotel Management, 2002)
Sol. Let the number be x. Then, 7x - 15 = 2x + 10 => 5x = 25 =>x = 5.
Hence, the required number is 5.
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Ex. 3. The sum of a rational number and its reciprocal is 13/6. Find the number.
Sol. Let the number be x.
(S.S.C. 2000)
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Then, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x2 – 13x + 6 = 0
=> 6x2 – 9x – 4x + 6 = 0 => (3x – 2) (2x – 3) = 0
x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.
Ex. 4. The sum of two numbers is 184. If one-third of the one exceeds one-seventh
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of the other by 8, find the smaller number.
Sol. Let the numbers be x and (184 - x). Then,
(X/3) - ((184 – x)/7) = 8 => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.
Ex. 5. The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.
Sol. Let the number be x and y. Then,
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x – y = 11 ----(i) and 1/5 (x + y) = 9 => x + y = 45 ----(ii)
Adding (i) and (ii), we get: 2x = 56 or x = 28. Putting x = 28 in (i), we get: y = 17.
Hence, the numbers are 28 and 17.
Ex. 6. If the sum of two numbers is 42 and their product is 437, then find the
absolute difference between the numbers. (S.S.C. 2003)
Sol. Let the numbers be x and y. Then, x + y = 42 and xy = 437
x - y = sqrt[(x + y)2 - 4xy] = sqrt[(42)2 - 4 x 437 ] = sqrt[1764 – 1748] = sqrt[16] = 4.
Required difference = 4.
2. Ex. 7. The sum of two numbers is 16 and the sum of their squares is 113. Find the
numbers.
Sol. Let the numbers be x and (15 - x).
Then, x2 + (15 - x)2 = 113 => x2 + 225 + X2 - 30x = 113
=> 2x2 - 30x + 112 = 0 => x2 - 15x + 56 = 0
=> (x - 7) (x - 8) = 0 => x = 7 or x = 8.
So, the numbers are 7 and 8.
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Ex. 8. The average of four consecutive even numbers is 27. Find the largest of these
numbers.
Sol. Let the four consecutive even numbers be x, x + 2, x + 4 and x + 6.
Then, sum of these numbers = (27 x 4) = 108.
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So, x + (x + 2) + (x + 4) + (x + 6) = 108 or 4x = 96 or x = 24.
:. Largest number = (x + 6) = 30.
Ex. 9. The sum of the squares of three consecutive odd numbers is 2531.Find the
numbers.
Sol. Let the numbers be x, x + 2 and x + 4.
Then, X2 + (x + 2)2 + (x + 4)2 = 2531 => 3x2 + 12x - 2511 = 0
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=> X2 + 4x - 837 = 0 => (x - 27) (x + 31) = 0 => x = 27.
Hence, the required numbers are 27, 29 and 31.
Ex. 10. Of two numbers, 4 times the smaller one is less then 3 times the 1arger one by 5. If the
sum of the numbers is larger than 6 times their difference by 6, find the two numbers.
Sol. Let the numbers be x and y, such that x > y
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Then, 3x - 4y = 5 ...(i) and (x + y) - 6 (x - y) = 6 => -5x + 7y = 6 …(ii)
Solving (i) and (ii), we get: x = 59 and y = 43.
Hence, the required numbers are 59 and 43.
Ex. 11. The ratio between a two-digit number and the sum of the digits of that
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number is 4 : 1.If the digit in the unit's place is 3 more than the digit in the ten’s place, what
is the number?
Sol. Let the ten's digit be x. Then, unit's digit = (x + 3).
Sum of the digits = x + (x + 3) = 2x + 3. Number = l0x + (x + 3) = llx + 3.
11x+3 / 2x + 3 = 4 / 1 => 1lx + 3 = 4 (2x + 3) => 3x = 9 => x = 3.
Hence, required number = 11x + 3 = 36.
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Ex. 12. A number consists of two digits. The sum of the digits is 9. If 63 is subtracted
from the number, its digits are interchanged. Find the number.
Sol. Let the ten's digit be x. Then, unit's digit = (9 - x).
Number = l0x + (9 - x) = 9x + 9.
Number obtained by reversing the digits = 10 (9 - x) + x = 90 - 9x.
therefore, (9x + 9) - 63 = 90 - 9x => 18x = 144 => x = 8.
So, ten's digit = 8 and unit's digit = 1.
Hence, the required number is 81.
Ex. 13. A fraction becomes 2/3 when 1 is added to both, its numerator and denominator.
3. And ,it becomes 1/2 when 1 is subtracted from both the numerator and denominator. Find
the fraction.
Sol. Let the required fraction be x/y. Then,
x+1 / y+1 = 2 / 3 => 3x – 2y = - 1 …(i) and x – 1 / y – 1 = 1 / 2
2x – y = 1 …(ii)
Solving (i) and (ii), we get : x = 3 , y = 5
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therefore, Required fraction= 3 / 5.
Ex. 14. 50 is divided into two parts such that the sum of their reciprocals is 1/ 12.Find the two
parts.
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Sol. Let the two parts be x and (50 - x).
Then, 1 / x + 1 / (50 – x) = 1 / 12 => (50 – x + x) / x ( 50 – x) = 1 / 12
=> x2 – 50x + 600 = 0 => (x – 30) ( x – 20) = 0 => x = 30 or x = 20.
So, the parts are 30 and 20.
Ex. 15. If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the
numbers )
Sol.
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Let the numbers be x, y and z. Then,
x+ y = 10 ...(i) y + z = 19 ...(ii) x + z = 21 …(iii)
Adding (i) ,(ii) and (iii), we get: 2 (x + y + z ) = 50 or (x + y + z) = 25.
Thus, x= (25 - 19) = 6; y = (25 - 21) = 4; z = (25 - 10) = 15.
Hence, the required numbers are 6, 4 and 15.
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