/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1211 The sum of the digits of a two-d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 42: Problem 1211

The sum of the digits of a two-digit number is 9 . The number is equal to 9 times the units' digit. Find the number.

Short Answer

Expert verified
The two-digit number is \(45\) as its digits add up to 9 and it is equal to 9 times its units' digit.

Step by step solution

01

Express the number in algebraic form

We represent the two-digit number using variables and the sum of the digits.\[ 10a + b = N \] where N is the given two-digit number, a is the tens digit, and b is the units digit.
02

Represent the given conditions as equations

We have two conditions: 1. The sum of the digits of the two-digit number is 9. Therefore, we can write an equation as: \(a + b = 9\) 2. The number is equal to 9 times the units' digit. So, the equation will be: \(N = 9b\)
03

Express N in terms of a and b

Now, as we have the expression of N in terms of a and b, we can write: \[ 10a + b = 9b \]
04

Substitute and solve for a and b

Substitute the value of a from the first equation into the second equation: \[ 10(9 - b) + b = 9b \] Expand and solve for b: \[ 90 - 10b + b = 9b \] \[ 90 - 9b = 9b \] \[ 90 = 18b \] Then, find the value of b: \[ b = \frac{90}{18} = 5 \] Now, find the value of a: \[ a = 9 - b = 9 - 5 = 4 \]
05

Write the two-digit number

Since we found a = 4 and b = 5, the two-digit number can be written as: \[ N = 10a + b = 10(4) + 5 = 45 \] The two-digit number in question is \(45\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Separate 120 into two parts such that the larger exceeds three times the smaller by 12 .

Show that the sum of any positive number and its reciprocal can not be less than \(2 .\)

The sum of a number and its reciprocal is \(65 / 28\). What is the number?

If 3 is subtracted from the numerator of a certain fraction, the value of the fraction becomes \(3 / 5 .\) If 1 is subtracted from the denominator of the same fraction then the value of the fraction becomes \(2 / 3\). Find the original fraction.

The product of two consecutive odd integers is 35 . Find the integers.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.