Question

(a)Find two consecutive odd integers such that the sum of the smallest integer and twice the greater integer is 85.

(b) The sum of three integer is 40.The second integer is three times the first and the third integer exceeds the second by 5.Find the three integers.

Answer 1

see explanation

Explanation:

(a)

let the two consecutive odd integers ne n and n + 2 , then

n + 2(n + 2) = 85

n + 2n + 4 = 85

3n + 4 = 85 ( subtract 4 from both sides )

3n = 81 ( divide both sides by 3 )

n = 27

n + 2 = 27 + 2 = 29

the 2 consecutive odd integers are 27 and 29

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(b)

let the first integer be n , then 2nd integer is 3n and 3rd is 3n + 5 , so

n + 3n + 3n + 5 = 40

7n + 5 = 40 ( subtract 5 from both sides )

7n = 35 ( divide both sides by 7 )

n = 5

3n = 3 × 5 = 15

3n + 5 = 15 + 5 = 20

the 3 integers are 5, 15, 20