The sum of two numbers is 45 and the mean proportional between them is 18. The numbers are:

a) (15, 30)

b) (32, 13)

c) (36, 9)

d) (25, 20)

The two numbers that add up to 45 and have a mean proportional of 18 are 36 and 9. Therefore, the correct option is c) (36, 9). The calculations involve solving a quadratic equation derived from the sum and mean conditions.
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Answered by Anonymous | 2025-07-04

To solve this problem, we need to identify two numbers that meet the given conditions: their sum is 45, and their mean proportional is 18.
The mean proportional (also known as the geometric mean) between two numbers, say a and b , is given by the formula:
a × b ​ = 18
We also know from the problem statement that:
a + b = 45
Let's test each pair of the provided multiple choice options to see which one satisfies both conditions:

Option (a) (15, 30):

Sum: 15 + 30 = 45
Mean Proportional: 15 × 30 ​ = 450 ​ = 21.21

This does not satisfy the mean proportional condition.

Option (b) (32, 13):

Sum: 32 + 13 = 45
Mean Proportional: 32 × 13 ​ = 416 ​ ≈ 20.4

This does not satisfy the mean proportional condition.

Option (c) (36, 9):

Sum: 36 + 9 = 45
Mean Proportional: 36 × 9 ​ = 324 ​ = 18

This satisfies both conditions. The sum is 45 and the mean proportional is indeed 18.

Option (d) (25, 20):

Sum: 25 + 20 = 45
Mean Proportional: 25 × 20 ​ = 500 ​ = 22.36

This does not satisfy the mean proportional condition.


Thus, the correct option is (c) (36, 9), as this pair of numbers satisfies both the condition of the sum being 45 and the mean proportional being 18.

Answered by danjohnbrain | 2025-07-06