Question

the sum of three numbers is 14. Three times the smallest is 1 less than the largest, while the sum of the largest and smallest is 9. Use a linear system in three variables to find the three numbers. The three numbers are , , and .

Answer 1

2, 5, 7.

Explanation:

call the smallest number A and the largest C.

we have A + B + C = 14.

Three times the smallest is 1 less than the largest:

3A = C - 1, C = 3A + 1.

sum of the largest and smallest is 9:

A + C = 9, C = 9 - A.

so we have C = 3A + 1 = 9 - A.

3A + A = 9 - 1

4A = 8

A = 2.

C = 9 - A = 9 - 2 = 7.

A + B + C = 14,

B = 14 - A - C = 14 - 2 - 7 = 5.

So A = 2, B = 5 and C = 7.