Math Problem Statement

a two digit number is a such that the digit at the one place is 4 more than the tens place the ratio of these number and number formed by reversing its digits is 47 find the number

Solution

Let's denote the two-digit number as NN, and let the tens digit be xx and the ones digit be yy.

From the problem statement, we have the following conditions:

  1. The digit at the ones place is 4 more than the tens place: y=x+4y = x + 4

  2. The ratio of the number NN and the number formed by reversing its digits is 47. The number NN can be written as: N=10x+yN = 10x + y The number formed by reversing the digits would be: Reversed number=10y+x\text{Reversed number} = 10y + x The given ratio is: NReversed number=47\frac{N}{\text{Reversed number}} = 47 Substituting the expressions for NN and the reversed number: 10x+y10y+x=47\frac{10x + y}{10y + x} = 47

Now, substitute y=x+4y = x + 4 into this equation: 10x+(x+4)10(x+4)+x=47\frac{10x + (x + 4)}{10(x + 4) + x} = 47 Simplifying the numerator and denominator: 10x+x+410x+40+x=47\frac{10x + x + 4}{10x + 40 + x} = 47 11x+411x+40=47\frac{11x + 4}{11x + 40} = 47

Now, cross-multiply to solve for xx: 11x+4=47(11x+40)11x + 4 = 47(11x + 40) 11x+4=517x+188011x + 4 = 517x + 1880 41880=517x11x4 - 1880 = 517x - 11x 1876=506x-1876 = 506x x=1876506=3.71x = \frac{-1876}{506} = -3.71

It seems there was a miscalculation in some part of the problem. Let me verify this!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Ratio and Proportions

Formulas

N = 10x + y
Reversed number = 10y + x
Ratio = N / Reversed number

Theorems

Basic algebraic manipulation
Ratio and proportion

Suitable Grade Level

Grades 7-9