Question

Three times a larger number is 30 more than 5 times a smaller number. The sum of the larger number and 5 times the smaller number is 50. Let x be the smaller number and y be the larger number. Create a system and graph it to find the solution. What are the two numbers?

Answer 1

Answer:

Three times a larger number is 30 more than 5 times a smaller number. The sum of the larger number and 5 times the smaller number is 50. Let x be the smaller number and y be the larger number. Create a system and graph it to find the solution. What are the two numbers?

Step-by-step explanation:

If "y" is the largest number, and "x" the smallest number, it would look like this:

3y = 5x + 30, we cleared to add the two equations and it would be: 3y - 5x = 30

y + 5x = 50

Where: 3y + y - 5x + 5x = 30 + 50

4y = 80; y = 80/4 = 20 = y

Now substituting the value of y in the equation would be: 20 + 5x = 50; 5x = 50-20; 5x = 30; x = 30/5 = 6 = x

And the two values would be: 6 and 20

Answer 2

3y  = 5x + 30

y + 5x = 50 .......(1)

3y - 5x = 30 .....(2)        - rearranging the first equation.

Add (1) and (2):-

4y = 80

y = 20  
Now plug y = 20 into equation (1):-
20 + 5x = 50
5x = 30 
x = 6

The 2 numbers are 6 and 20.