SOLUTION: The sum of three numbers is 15. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 49. The difference between 3 times the

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Question 1131188: The sum of three numbers is 15. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 49. The difference between 3 times the first number and the second number is 16. Find the three numbers.
Found 3 solutions by greenestamps, ankor@dixie-net.com, MathTherapy:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


When you submit a question without saying anything about what work you have tried to do on the problem (as you are asked to), we have no idea what part of it is giving you trouble. And it might also be that you didn't do any work yourself and just want us to do it for you; that's not what this forum is for.

I'll translate the given information into equations for you and suggest a path you can follow to the solution. If my response is not what you need, then post the question again, showing what you have done and being specific about what you need help with.

(1) The sum of three numbers is 15.



(2) The sum of twice the first number, 4 times the second number, and 5 times the third number is 49.



(3) The difference between 3 times the first number and the second number is 16.



Since the third equation involves only x and y, my suggestion for how to get started on solving the problem would be to eliminate z between the first and second equations; then you will have two equations in x and y that you can solve by your favorite method. Then knowing the values of x and y you can use any one of the original equations to solve for z.
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The sum of three numbers is 15.
a + b + c = 15
The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 49.
2a + 4b + 5c = 49
The difference between 3 times the first number and the second number is 16.
3a - b = 16
:
Find the three numbers.
:
Add the 1st and the 3rd equations
a + b + c = 15
3a -b + 0 = 16
-----------------adding eliminates b
4a + 0 + c = 31
4a + c = 31
:
multiply the 1st equation by 4 and subtract the 2nd equation
4a + 4b + 4c = 60
2a + 4b + 5c = 49
-------------------subtraction eliminates b
2a + 0 - c = 11
2a - c = 11
:
Add the two resulting equations
4a + c = 31
2a - c = 11
----------------adding eliminates c, find a
6a + 0 = 42
a = 42/6
a = 7
:
use the 3rd equation to find b
3a - b = 16
3(7) - b = 16
-b = 16 - 21
-b = -5
b = 5
:
Find c using the 1st equation
7 + 5 + c = 15
c = 15 - 12
c = 3
:
:
Chck solutions in the 2nd equation
2(7) + 4(5) + 5(3) =
14 + 20 + 15 = 49
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

The sum of three numbers is 15. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 49. The difference between 3 times the first number and the second number is 16. Find the three numbers.
Let 1st, 2nd, and 3rd numbers be F, S, and T, respectively

Then we get: 

F + 3F - 16 + T = 15 ------ Substituting 3F - 16 for S in eq (i)

4F + T = 31 ------ eq (iv)



2F + 4(3F - 16) + 5T = 49 -- Substituting 3F - 16 for S in eq (ii)

14F + 5T = 113 ------------- eq (v)

 - 20F - 5T = - 155 -------- Multiplying eq (iv) by - 5 ------ eq (vi)

 - 6F = - 42 --------------- Adding eqs (vi) & (v)

 

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