The sum of three numbers is 16. The sum of twice the first number, 5 times the second number, and 6 times the third number is 67. The differenz between 8 times the first number and the second number is 55. Find the three numbers.

Lösung

T h e s u m o f t h ree n u mb ers i s 16. 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 67. T h e d i ff ere n ce b e tw ee n 8 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 55. F in d t h e t h ree n u mb ers .

The numbers : 7, 1, 8

Schritte zur Lösung

Represent the numbers with

x, y, z

number 1 : x

number 2 : y

number 3 : z

A.T.Q.:

x + y + z = 16

2 x + 5 y + 6 z = 67

8 x - y = 55

x + y + z = 16, 2 x + 5 y + 6 z = 67, 8 x - y = 55 : x = 7, y = 1, z = 8

The numbers : 7, 1, 8