The difference between two numbers is 35. 1/2 the larger number plus 1/3 the smaller is 30. What are the numbers?

Question

Its 8-2 solving problems. Algebra 1.Need to know the two numbers. 

Answer 1

Let x be the larger number

 

Let y be the smaller number

 

Then your 2 equations are:

 

x - y = 35

 

(1/2)x + 1/3(y) = 30

 

Let's use substitution for this system of equations. First, solve first equation for x to get:

 

x = 35 + y

 

Now substitute this into the second equation:

 

(1/2)(35 +y) + 1/3(y) = 30

 

Fastest way to clear this is to multiply both sides by 6

 

3(35+y) + 2y = 180

 

Now you have:

 

105 + 3y + 2y = 180

 

You can solve for y to get y.  Plug y in either equation to get x.

 

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Answer 2

The difference between two numbers is 35:

x - y = 35 _____ eqn 1

 

1/2 the larger number plus 1/3 the smaller is 30:

x/2 + y/3 = 30

multiply through by 6 to clear fractions

3x + 2y = 180 _____ eqn 2

 

Our system of equations is thus:

x - y = 35

3x + 2y = 180

 

multiply equation 1 by 2 and add equations

to eliminate the y variable and solve for x.

 

2x - 2y = 70

3x + 2y = 180

---------------------

5x = 250

x = 50

 

50 - y = 35

y = 15

 

The numbers are {15, 50}