SOLUTION: The sum of three numbers is 10. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 33. The difference between 6 times the f

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Question 1124158: The sum of three numbers is 10. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 19. Find the three numbers.
first​ number:

second​ number:

third​ number:


**** No decimal number it has to be a whole number for the answer*****
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

let’s three numbers be , , and

if the sum of three numbers is , we have
........eq.1


if the sum of the first​ number, times the second​ number, and times the third number is , we have
........eq.2


if the between times the first number and the second number is , we have
..............eq.3 ....solve for
..........eq.a


go to ........eq.2, substitute



....solve for

.........eq.b


go to ........eq.1 substitute and

....solve for









go to ..........eq.a , plug in for





go to .........eq.b , plug in for







Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The sum of three numbers is 10. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 33. The difference between 6 times the first number and the second number is 19. Find the three numbers.
first​ number:

second​ number:

third​ number:


**** No decimal number it has to be a whole number for the answer***** 
Let the 1st, 2nd and 3rd numbers be F, S, and T, respectively

Then: F + S + T = 10 --------- eq (i)

Also, 2F + 4S + 5t = 33 ------ eq (ii)

And, 6F - S = 19____S = 6F - 19 ------- eq (iii)

F + 6F - 19 + T = 10_____7F + T = 29______T = 29 - 7F -------- Substituting 6F - 19 for S in eq (i) ------- eq (iv)

2F + 4(6F - 19) + 5T = 33_____2F + 24F - 76 + 5T = 33_____26F + 5T = 109 -------- Substituting 6F - 19 for S in eq (ii) ------- eq (v)

26F + 5(29 - 7F) = 109 ------- Substituting 29 - 7F for T in eq (v)

26F + 145 - 35F = 109

- 9F = - 36

F, or 1st number =  

S = 6(4) - 19 --------- Substituting 4 for F in eq ((iv)

S, or 2nd number = 

T = 29 - 7(4) ------ Substituting 4 for F in eq (iv)

T, or 3rd number =  

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