The sum of two numbers is 21. The smaller number is three more than half the larger number. What are the two numbers

X = 12 and Y = 9

Step-by-step explanation:

Equations:

The sum of two numbers is 21

X + Y = 21

The smaller number is three more (+3) than half (1/2) of the larger number (X)

Y = (X/2) + 3

Solve for X:

X + Y = 21

- Use Substitution

X + ((X/2) + 3) = 21

X + (X/2) + 3 = 21

- Make X have the same denominator

(2X/2) + (X/2) + 3 = 21

- Subtract 3

(2X/2) + (X/2) = 18

- Add Both Fractions

(3X/2) = 18

- Multiply by 2

3X = 36

- Divide by 3

X = 12

Solve for Y:

Y = (X/2) + 3

- Use Substitution

Y = (12/2) + 3

Y = 6 + 3

Y = 9

y = 12

x = 9

Step-by-step explanation:

y=larger number

(y/2 + 3) + y = 21

Step 1: Simplify both sides of the equation.

y / 2 + 3+y=21

1 / 2 y+3+y=21

(1 / 2 y+y) + (3) = 21 (Combine Like Terms)

3 / 2 y+3=21

3 / 2 y+3=21

Step 2: Subtract 3 from both sides.

3 / 2 y+3-3=21-3

3 / 2 y=18

Step 3: Multiply both sides by 2/3.

(2 / 3) * (3 / 2 y) = (2 / 3) * (18)

y=12