The sum of three numbers is 15. The sum of twice the first number, 5 times the second number, and 6 times the third number is 56. The difference between 5 times the first number and the second number is 29. Find the three numbers.

Solution

T h e s u m o f t h ree n u mb ers i s 15. T h e s u m o f tw i ce t h e f i rs t n u mb er, 5 t im es t h e seco n d n u mb er, an d 6 t im es t h e t hi r d n u mb er i s 56. T h e d i ff ere n ce b e tw ee n 5 t im es t h e f i rs t n u mb er an d t h e seco n d n u mb er i s 29. F in d t h e t h ree n u mb ers .

The numbers : 7, 6, 2

Solution steps

Represent the numbers with

x, y, z

number 1 : x

number 2 : y

number 3 : z

A.T.Q.:

x + y + z = 15

2 x + 5 y + 6 z = 56

5 x - y = 29

x + y + z = 15, 2 x + 5 y + 6 z = 56, 5 x - y = 29 : x = 7, y = 6, z = 2

The numbers : 7, 6, 2