SOLUTION: A number is 4 more than another. If thrice the larger number is divided by the smaller, the quotient is 5 and the remainder is 6. What are the numbers?

Question 935699: A number is 4 more than another. If thrice the larger number is divided by the smaller, the quotient is 5 and the remainder is 6. What are the numbers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the larger number.
y is the smaller number.
x = y + 4 means that the larger number is 4 more than the smaller number.
3x/y = 5 with a remainder of 6 means three times the larger number divided by the smaller number is equal to 5 with a remainder of 6.
3x/y = 5 with a remainder of 6 can also be shown as 3x/y = 5 + 6/y.
you have 2 equations that need to be solved simultaneously.
they are:
x = y + 4
3x/y = 5 + 6/y
replace x with y + 4 in the second equation to get:
3(y+4)/y = 5 + 6/y
multiply both sides of this equation by y to get:
3(y+4) = 5y + 6
distribute the multiplication to get:
3y + 12 = 5y + 6
subtract 3y from both sides of this equation and subtract 6 from both sides of this equation to get:
6 = 2y
solve for y to get:
y = 3
if y = 3, then x must be equal to 4.
that's your solution.
you need to go back to the original equations to confirm the solution is correct.
x = y + 4 becomes 7 = 3 + 4 which is correct.
3x/y = 5 + 6/y becomes 3(7)/3 = 5 + 6/3 which becomes 21/3 = 5 + 2 which becomes 7 = 7 which is also correct.
the solution looks good.
there was a wrinkle in there because 21/3 = 7 with a remainder of 0.
that would cause confusion and make you think that the solution is not correct, but:
21/3 = 5 with a remainder of 6 is equivalent to 21/3 = 7, so the solution is correct even if the confirmation looks odd.

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