SOLUTION: The quotient of two numbers is 12 and their sum is 91. Find the two numbers that satisfy the condition.

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:

RELATED QUESTIONS
The Sum of Two numbers is 44 and their quotient is 3/8. Find the numbers (answered by Bastian21)

Two numbers are in the ratio 3:4.Find the numbers if their sum is 91 (answered by vheroli)

The sum of two numbers is 70. Their quotient is 13. what are the two... (answered by Fombitz)

the product of two numbers is 36 and their quotient is 9. find the numbers. (answered by 428225)

The product of two numbers is 36 and their quotient is 9.Find the... (answered by josgarithmetic)

the product of two numbers is 36 and their quotient is 9.Find the numbers. (answered by Alan3354,KMST)

The sum of two numbers is 18. The sum of their squares is at most 170. Find all integral... (answered by Fombitz)

Two numbers have a sum of 64. Their quotient is 7. What are the two... (answered by josmiceli)

The product of two numbers is 36 and their quotient is9.Find the... (answered by math_helper)