The sum of two numbers is 7. Three times one of the numbers is 15 more than the other number. Find the numbers.

Answer 1

The sum of two numbers is 7. Three times one of the numbers is 15 more than the other number. Find the numbers.

Let X and Y be the two numbers.

X + Y = 7 "The sum of two numbers is 7."

3X = Y + 15 "Three times one of the numbers is 15 more than the other number."

Taking the TOP EQUATION and solving for X:

X + Y = 7

X = 7 - Y Subtracting Y from both sides of the equation.

Plugging 7 - Y into the BOTTOM EQUATION for X:

3X = Y + 15

3(7 - Y) = Y + 15

21 - 3Y = Y + 15 Distribute 3 times (7 - Y)

-3Y = Y + 15 - 21 Subtracting 21 from both sides of the equation.

-3Y = Y - 6 15 - 21 = -6

-4Y = - 6 Subtracting Y from both sides of the equation.

Y = - 6/ - 4 Dividing both sides of the equation by - 4.

Y = 3/2 or 1.5

Plugging 3/2 into the TOP EQUATION for Y to solve for X:

X + Y = 7

X + 3/2 = 7

X = 7 - 3/2 Subtracting 3/2 from both sides of the equation.

X = 14/2 - 3/2 = 11/2 = 5.5

ANSWER: ONE NUMBER IS 1.5 AND THE OTHER NUMBER IS 5.5

CHECKING:

TOP EQUATION: X + Y = 7

5.5 + 1.5 = 7 Yes!

BOTTOM EQUATION: 3X = Y + 15

3(5.5) = 1.5 + 15

16.5 = 16.5 Yes!

Hope this helps you JA.