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Answer:

Manuel is 19 and Gupta is 12

Step-by-step explanation:

Use the word problem to set up 2 equations.

2x-5=y

x+y=31

Now solve these as a set of equations:

2x-5=y

x-31=-y

Add them together to get:

3x-36=0

so 3x=36 so x=12

Now plug in to get y: y=31-12=19

So x=12 and y=19

Answer: The age of Gupta and Manuel are 12 years and 19 years respectively.

Step-by-step explanation:

Let the age of Gupta would be x.

Let the age of Manuel would be 2x-5.

According to question, the sum of Manuel and Gupta = 31.

So, it becomes,

[tex]x+2x-5=31\\\\3x-5=31\\\\3x=31+5\\\\3x=36\\\\x=\dfrac{36}{3}\\\\x=12[/tex]

Hence, the age of Gupta would be 12 years old and age of Manuel would be [tex]2x-5=2(12)-5=24-5=19[/tex]

Therefore, the age of Gupta and Manuel are 12 years and 19 years respectively.

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