Answer: 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!
Explanation: