word problem

Question

The sum of two numbers is 29. The sum of the smaller and 4 times the larger is 80. Find the numbers.

Answer 1

Hi Valerie, let x be the smaller number and y the larger number. Set up two equations:

 

x + y = 29 and x + 4y = 80

 

Solve by elimination:

 

x  +   y = 29

x  + 4y = 80

 

Multiply the first equation by -1

 

-x  -   y = -29

 x  + 4y =  80

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Add the two equations to eliminate the x variable:

 

3y = 51

 

Divide both sides by 3:

 

y = 17

 

The larger number is 17.

 

Replace y in the first equation to solve for x:

 

x + 17 = 29

 

Subtract 17 from both sides:

 

x = 12

 

The smaller number is 12

 

Check:

 

12 + 17 = 29

 

29 = 29

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

 

12 + (4 * 17) = 80

 

12 + 68 = 80

 

80 = 80

 

Questions?