Question

The sum of two numbers is 27. One number is 2 times as large as the other. What are the numbers?

Larger number:
Smaller number: ​

Answer 1

Let x be the larger number, and y be the smaller number.

The sum of two numbers is 27. So the equation would be:

x+y=27

The larger number is 3 more than the smaller number. So:

larger number = smaller number + 3

or

x=y+3

Now, we want to get rid of x and solve for y first. Since x=y+3, we can substitute y+3 for x in the equation x+y=27.

Therefore:

(y + 3) + y = 27

Combine like terms:

2y + 3 = 27

Subtract 3 on both sides:

2y = 24

Divide both sides by 2:

y = 12

So the smaller number is 12. The larger number is 3 more than the smaller number, so:

x = 12 + 3

x = 15

The 2 numbers are 12 and 15. Check:

12 + 15 = 27

Answer 2

Larger number: 18

Smaller number: ​9

Explanation:

a + b = 27

----------------------------

a = b × 2

----------------------------

a + b = 27

(b × 2) + b = 27

2b + b = 27

3b = 27

3b ÷ 3 = 27 ÷ 3

b = 9

----------------------------

a = b × 2

a = (9) × 2

a = 18

----------------------------

a + b =27

(18) + (9) = 27

27 = 27