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Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers

User Piertoni
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1 Answer

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Explanation:

two consecutive numbers means that one is larger by 1 than the other number.

so, we have to choices depending on whether the first number (multiplied by 3) is the larger one, or the second number.

to show what I mean, let's start with the second number being the larger one.

we are dealing therefore with x and (x+1).

3x + (x+1) - 2 = 144

4x - 1 = 144

4x = 145

x = 145/4

this is not an integer (but this is necessary to have 2 dedicated consecutive numbers).

so, it is actually not a valid solution.

therefore we are checking the other approach :

we are dealing therefore still with x and (x+1). but now we multiply the other number by 3.

3(x+1) + x - 2 = 144

4x + 1 = 144

4x = 143

x = 143/4

this is still not an integer (but this is necessary to have 2 dedicated consecutive numbers).

so, it is actually not a valid solution either.

and now I am beginning to think you left out some important information in the question.

could it be these 2 numbers are consecutive even or consecutive uneven numbers ?

because then the difference between the both of them is 2 and not 1.

we are dealing therefore with x and (x+2). first attempt to make the smaller number the "first" number :

3x + (x+2) - 2 = 144

4x = 144

x = 144/4 = 36

ah ! now that looks different !

36 and 38 are valid solutions under the changed assumptions. and we are dealing with consecutive even numbers.

let's check :

36×3 + 38 - 2 = 36×3 + 36 = 36×4 = 144

correct.

and fun fact, if we turn this around and make the larger number the "first" number, we are still dealing with x and (x+2), but now we multiply the larger number by 3 :

3(x+2) + x - 2 = 144

4x + 6 - 2 = 144

4x + 4 = 144

4x = 140

x = 140/4 = 35

35 and 37 are also valid solutions under the new assumptions and two consecutive uneven numbers ...

so, please check what your original question (and maybe the headlines and description around it) says. and then pick the right solution.

User Neil Stockton
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