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

Larger number = 6.

Smaller number = 2.

Step-by-step 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.

6 and 2

Step-by-step 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