Question 202612: The quotient of two numbers is 12 and their sum is 91. Find the two numbers that satisfy the condition. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! Using "x" and "y" for the two numbers we are trying to find, let's start by writing equations which express the information you are given. The quotient of two numbers is 12:
and their sum is 91
We have two equations with two variables. Generally we should be able to solve the system. The first equation is not linear but the second one is. Probably the easiest way to solve this system is to solve the linear equation for either of the variables and then substitute for that variable in the other equation.
Solving the second equation for y we get:
Substituting into the first equation we get:
Now we can solve this for x. First we'll get rid of the fraction by multiplying both sides of the equation by the denominator:
On the left the (-x + 91)'s cancel and on the right we use the Distributive Property to multiply:
Now get x on one side by adding 12x to both sides giving:
Now change the 13 to a one by dividing both sides by 13:
And finally substitute this value for x, in either equation, to find the value for y:
Subtract 84 from both sides:
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