Question

3.3.31

Skill Builde
The sum of two numbers is 8. Five times the larger number plus four times the smaller number is 38. Find the numbers
The larger number is
and the smaller number is

Answer 1

Larger number = 6.

Smaller number = 2.

Explanation:

Let the lower number be x then the other number = 8-x.

Also;

5(8 - x) + 4x = 38

40 - 5x + 4x = 38

-x = -2

x = 2 = lower number.

Larger number = 8 - 2 = 6.

Answer 2

6 and 2

Explanation:

let the 2 numbers be x and y with x > y, then

x + y = 8 → (1)

5x + 4y = 38 → (2)

Rearrange (1) expressing x in terms of y by subtracting y from both sides

x = 8 - y → (3)

Substitute x = 8 - y into (2)

5(8 - y) + 4y = 38 ← distribute and simplify left side

40 - 5y + 4y = 38

40 - y = 38 ( subtract 40 from both sides )

- y = - 2 ( multiply both sides by - 1 )

y = 2

Substitute y = 2 into (3) for corresponding value of x

x = 8 - 2 = 6

The larger number is 6 and the smaller number is 2