Question 1066221
"the sum of two numbers is 18" means that we have two unknown numbers, call them x and y for now, that add up to 18


so {{{x+y = 18}}}


Solve for y to get {{{y = 18-x}}} (I subtracted x from both sides)


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Let's say that x is the greater number. So x > y. 


"Three times the greater number exceeds four times the smaller number by 5"

translates to

"three times x is equal to (4 times y) plus 5"

which creates this equation

{{{3x = 4y+5}}}


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We'll plug the equation {{{y = 18-x}}} into the second equation we just got. Then solve for x.


{{{3x = 4y+5}}}


{{{3x = 4(18-x)+5}}} Replace y with 18-x


{{{3x = 72-4x+5}}}


{{{3x = 77-4x}}}


{{{3x+4x = 77-4x+4x}}} Add 4x to both sides


{{{7x = 77}}}


{{{7x/7 = 77/7}}} Divide both sides by 7


{{{x = 11}}}


One of the numbers, the larger number, is 11.


Use this to find y
{{{y = 18-x}}}
{{{y = 18-11}}}
{{{y = 7}}}
The other number is 7


In summary, the two numbers are 7 and 11. 


Side note: The instruction "find the number" is too vague since it previously mentions two numbers.