In a two-digit number, the unit's digit is 7 more than the ten's digit. Sum of the digits is half of the whole number. Find the digits and number.
solution to Example 1 of Algebra Word Problem :
Let x be the ten's digit of the two-digit number. Then its unit's digit = x + 7. We know the value of a two-digit number = its unit's digit + 10(its ten's digit). ∴ the number = (x + 7) + 10(x) = 11x + 7. Sum of the digits = (x + 7) + (x) = 2x + 7. By data, Sum of the digits is half of the whole number ∴ 2x + 7 = (1⁄2)(11x + 7).
This is the Linear Equation formed by converting the given word statements to the symbolic language.
Now we have to solve this equation. Multiplying both sides with 2, we get 2(2x + 7) = 2(1⁄2)(11x + 7) ⇒ 2 x 2x + 2 x 7 = 11x + 7 ⇒ 4x + 14 = 11x + 7 ⇒ 4x - 11x = 7 - 14 ⇒ -7x = -7 ⇒ x = (-7)⁄(-7) ⇒ x = 1. ∴ten's digit of the two-digit number = x = 1. Ans and unit's digit of the two-digit number = x + 7 = 1 + 7 = 8.Ans. ∴ the required number is 18. Ans.
Check: the number = 18 Sum of the digits = 1 + 8 = 9. = (1⁄2)18 = (1⁄2)the number (verified.)
Get The Best Grades With the Least Amount of Effort
Here is a collection of proven tips, tools and techniques to turn you into a super-achiever - even if you've never thought of yourself as a "gifted" student.
The secrets will help you absorb, digest and remember large chunks of information quickly and easily so you get the best grades with the least amount of effort.
If you apply what you read from the above collection, you can achieve best grades without giving up your fun, such as TV, surfing the net, playing video games or going out with friends!
In a two-digit number, unit's digit is 3 more than the ten's digit. The number formed by interchanging the digits and the original number are in the ratio 7:4. Find the number.
solution to Example 2 of Algebra Word Problem :
Let x be the ten's digit of the two-digit number. Then its unit's digit = x + 3. We know the value of a two-digit number = its unit's digit + 10(its ten's digit). ∴ the original number = (x + 3) + 10(x) = 11x + 3. The number formed by interchanging the digits = (x) + 10(x + 3) = x + 10x + 10 x 3 = 11x + 30. By data the ratio of the number formed by interchanging the digits and the original number is 7:4. ⇒ (11x + 30) : (11x + 3) = 7 : 4 ⇒ (11x + 30)⁄(11x + 3) = 7⁄4 cross multiplying, we get 4(11x + 30) = 7(11x + 3) ⇒ 4 x 11x + 4 x 30 = 7 x 11x + 7 x 3 ⇒ 44x + 120 = 77x + 21 ⇒ 44x - 77x = 21 - 120 ⇒ -33x = -99 ⇒ x = (-99)⁄(-33) = 3. ∴ten's digit of the two-digit number = x = 3. and unit's digit of the two-digit number = x + 3 = 3 + 3 = 6. ∴ the required number is 36. Ans.
Check: The original number = 36 The number formed by interchanging the digits = 63 Their ratio = 63 : 36 = 7 x 9 : 4 x 9 = 7 : 4 which is the given ratio. (verified.)
A person walks from one place to another place at a speed of 4km/hr. If he walks at a speed of 5km/hr, he reaches the place 7 minutes earlier. Find the distance between the two places.
solution to Example 3 of Algebra Word Problem :
Let x km be the distance between the two places. We know time = (distance)⁄(speed) ∴ the time taken to reach the place at a speed of 4km/hr = (xkm)⁄(4km/hr) = x⁄4.hrs. = (x⁄4) x 60 minutes. = 15x minutes. and the time taken to reach the place at a speed of 5km/hr = (xkm)⁄(5km/hr) = x⁄5.hrs. = (x⁄5) x 60 minutes. = 12x minutes. By data the time taken at 5km/hr is 7 minutes less than that at 4km/hr. That means 12x = 15x - 7
This is the Linear Equation formed by converting the given word statements to the symbolic language.
Now we have to solve this equation. ⇒ 12x - 15x = -7 ⇒ -3x = -7 ⇒ x = (-7)⁄(-3) = 7⁄3 ∴ The distance between the two places = x km = (7⁄3)km. Ans.
Check: The time taken to reach the place at a speed of 4km/hr = 15x = 15(7⁄3) = 5(7) = 35 minutes. The time taken to reach the place at a speed of 5km/hr = 12x = 12(7⁄3) = 4(7) = 28 minutes. = 35 minutes - 7 minutes which is as per data.(verified.)
Exercise on Algebra Word Problem
Solve each of the following Algebra Word problem.
In a two-digit number, the unit's digit is two more than ten's digit. Sum of the digits is equal to 1⁄4 of the whole number. Find the number.
In a two-digit number, the unit's digit is twice the ten's digit. If sum of the digits is added to the whole number, the result is equal to 30. Find the number.
Progressive Learning of Math : Algebra Word Problem
Recently, I have found a series of math curricula (Both Hard Copy and Digital Copy) developed by a Lady Teacher who taught everyone from Pre-K students to doctoral students and who is a Ph.D. in Mathematics Education.
This series is very different and advantageous over many of the traditional books available. These give students tools that other books do not. Other books just give practice. These teach students “tricks” and new ways to think.
These build a student’s new knowledge of concepts from their existing knowledge. These provide many pages of practice that gradually increases in difficulty and provide constant review.
These also provide teachers and parents with lessons on how to work with the child on the concepts.
The series is low to reasonably priced and include
Are you spending lot of money for math tutors to your child and still not satisfied with his/her grades ?
Do you feel that more time from the tutor and more personalized Math Help to identify and fix the problems faced by your child will help ?
Here is a fool proof solution I strongly recommend and that too With a minuscule fraction of the amount you spent on tutors with unconditional 100% money back Guarantee, if you are not satisfied.
It is like having an unlimited time from an excellent Tutor.
It is an Internet-based math tutoring software program that identifies exactly where your child needs help and then creates a personal instruction plan tailored to your child’s specific needs.
If your child can use a computer and access the Internet, he or she can use the program. And your child can access the program anytime from any computer with Internet access.
There is an exclusive, Parent Information Page provides YOU with detailed reports of your child’s progress so you can monitor your child’s success and give them encouragement. These Reports include
Time spent using the program
Assessment results
Personalized remediation curriculum designed for your child
Details the areas of weakness where your child needs additional help
Provides the REASONS WHY your child missed a concept
List of modules accessed and amount of time spent in each module
Quiz results
Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section of the program, available exclusively to you, the parent. The section is accessed by a password that YOU create and use. No unauthorized users can access this information.
Its research-based results have proven that it really works for all students! in improving math skills and a TWO LETTER GRADE INCREASE in math test scores!,if they invest time in using the program.
Proven for More than 10,000 U.S. public school students who increased their math scores.
