# Determine numbers (word problem)One number is 20 more than 2 times another number. If each number were multiplied by 2, their difference would be 116. What are the numbers?

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Let the number to be determined by x and y. Now it is given that one number is 20 more that twice the other.

=> x = 20 + 2y

If each number is multiplied by 2, their difference would be 116

=> 2x - 2y = 116

=> x - y = 58

Use x = 20 + 2y

=> 20 + 2y - y = 58

=> y = 38

x = 20 + 2*38 = 96

**The required numbers are 96 and 38**

**The numbers are 96 and 38.**

y = 2x + 20

2y - 2x = 116

Now you just substitute the value that is given for y in the first equation into the second equation.

2 (2x + 20) - 2x = 116

4x + 40 - 2x = 116

2x = 76

x = 38

Now substitute this value for x back into the first equation.

y = 76 + 20

y = 96

**So the two numbers are 96 and 38.**

We'll note the numbers as x and y.

We'll put as x the number that is 20 more than 2 times y.

We'll write the sentence mathematically:

x = 20 + 2y (1)

Now, we'll write mathematically the other constraint from enunciation:

2(x - y) = 116

We'll divide by 2;

x - y = 58

x = 58 + y (2)

We'll put (1) = (2):

20 + 2y = 58 + y

We'll isolate y to the left side:

2y - y = 58 - 20

y = 38

x = 58 + y

x = 58 + 38

x = 96

**The numbers are: x = 96 and y =38.**