algebra word problem

Question

The sum of two numbers is 34. The sum of the smaller and 5 times the larger is 142. Find the numbers.

Answer 1

Hi Stephen, let x represent the smaller number and y represent the larger number. Set up a system of equations to solve for x and y.

 

Equation 1:

 

x + y = 34

 

Equation 2:

 

x + 5y = 142

 

System of equations:

 

x  +   y =   34

x  + 5y = 142

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To solve, multiply the first equation by -1 and add.

 

-x  -    y = -34

 x  + 5y = 142

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4y = 108

 

y = 27

 

Substitute for y in the first equation:

 

x + 27 = 34

 

x = 7

 

Answer:

 

one number is 7 and the other number is 27.

 

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