Question

One number exceeds another number by 5. Two times the smaller number diminished by the greater number equals 9. Find the larger number.

Answer 1

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Answer 2

The larger number is 19

Given :

• One number exceeds another number by 5.

• Two times the smaller number diminished by the greater number equals 9.

To find :

The larger number

Solution :

Step 1 of 2 :

Form the equation to find the larger number

Here it is given that one number exceeds another number by 5.

Let the numbers are x and x + 5

∴ Larger number = x + 5 and smaller number = x

Now it is given that two times the smaller number diminished by the greater number equals 9

By the given condition

$\displaystyle \sf 2x - (x + 5) = 9$

Step 2 of 2 :

Find the larger number

$\displaystyle \sf 2x - (x + 5) = 9$

$\displaystyle \sf{ \implies }2x - x - 5 = 9$

$\displaystyle \sf{ \implies }x - 5 = 9$

$\displaystyle \sf{ \implies }x = 5 + 9$

$\displaystyle \sf{ \implies }x = 14$

Smaller number = x = 14

Larger number = x + 5 = 14 + 5 = 19

Hence larger number is 19

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