There are two numbers which sum to 10. If one number is five less than four times the other, find the numbers.

Answer 1

FIND THE TWO NUMBERS.

Let X = one of the two numbers

Let Y = the other number

The SUM of the two numbers is 10.

X + Y = 10

One number is 5 less than 4 times the other.

X = 4Y - 5

Now, substitute or plug 4Y - 5 into X in the equation and solve.

X + Y = 10

(4Y - 5) + Y = 10 (Plugging 4Y - 5 into X)

4Y + Y - 5 = 10 (Remove parenthesis and group)

5Y - 5 = 10 (Combining like terms)

5Y - 5 + 5 = 10 + 5 (Adding 5 to both sides)

5Y = 15

5Y/5 = 15/5 (Dividing both sides by 5)

Y = 15/5 (The 5's cancel each other out)

Y = 3

Now, solve for X.

Plug in 3 for Y in the equation X + Y = 10.

X + Y = 10

X + 3 = 10 (Substitution)

X + 3 - 3 = 10 - 3 (Subtracting 3 from both sides)

X = 7

ANSWER: X=7 AND Y=3

CHECKING:

X + Y = 10

7 + 3 = 10

DOES (4Y - 5) + Y = 10?

(4 * 3) - 5 + 3 = 12 - 5 + 3 = 7 + 3 = 10

YES IT DOES.