Question 279285
The Set-Up
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Let A = 10's Digit
Let B = 1's Digit

Equation 1: {{{N = 10A + B}}}
Equation 2: {{{A = B - 3}}}
Equation 3: {{{N + 2 = 7B}}}

Solution:
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Solve equation 3 for N
Equation 3: {{{N + 2 = 7B}}}
{{{N = 7B - 2}}}

Now substitute this and equation 2 into equation 1
Equation 1: {{{N = 10A + B}}}
{{{7B - 2 = 10*(B-3) + B}}} Simplify
{{{7B - 2 = 10B - 30 + B}}}
{{{7B - 2 = 11B - 30}}} Subtract 7B from both sides
{{{-2 = 4B - 30}}} Add 30 to both sides
{{{28 = 4B}}} Divide both sides by 4
{{{highlight(7 = B)}}}

Now plug 7 into equation 2 for B
Equation 2: {{{A = B - 3}}}
{{{A = 7 - 3}}}
{{{highlight(A = 4)}}}

Now substitute the values into equation 1
{{{N = 10A + B}}}
{{{N = 10*(4) + 7}}}
{{{N = 40 + 7}}}
{{{highlight(N = 47)}}}