SOLUTION: The quotient of two numbers is 6. If the greater number is decreased by eight, it is equal to four times the lesser number. What are the numbers?

Question 916515: The quotient of two numbers is 6. If the greater number is decreased by eight, it is equal to four times the lesser number. What are the numbers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a is the larger number
b is the smaller number
a/b = 6

a+8 = 4b
subtract 8 from both sides of the equation to get:
a = 4b-8

replace a with 4b-8 in the equation a/b = 6 to get:
(4b-8)/b = 6
multiply both sides of the equation by b to get:
4b-8 = 6b
subtract 4b from both sides of the equation to get:
-8 = 2b
divide both sides of the equation by 2 to get:
-4 = b which is the same as b = -4

since a = 4b-8, and b = -4, then you get:
a = 4(-4)-8 = -24

you have a = -24 and b = -4
a/b = 6 becomes -24/-4 = 6 which becomes 6 = 6
this confirms the values of a and b are good.

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