The four-digit number has a digit sum of 20. The sum of its last two digits is equal to its second digit increased by 5, the sum of its outer digits equals to its second digit decreased by 3. If we write the digits of the number in reverse order, the number increases by 2,178. Find the number.

The four-digit number has a digit sum of 20. The sum of its last two digits is equal to its second digit increased by 5, the sum of its outer digits equals to its second digit decreased by 3. If we write the digits of the number in reverse order, the number increases by 2,178. Find the number.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section: Chapter Questions

Problem 29CLR

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Solve the worded problem using matrix method.

The four-digit number has a digit sum of 20. The sum of its last two digits is equal to its second
digit increased by 5, the sum of its outer digits equals to its second digit decreased by 3. If we
write the digits of the number in reverse order, the number increases by 2,178. Find the number.

A cylinder made out of the yellow copper has the weight of 6.297 kg and the volume of 750
cm³. How many kilograms of copper and how many kilograms of zinc the cylinder contains ?
(The density of copper is 8,900 kg/m², the density of zinc is 7,100 kg/m³.)

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