The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number. Find the two numbers.

The value of the larger number, x, is 57. The value of the smaller number, y, is equal to 42.

x - y = 15

2x + 8 = 3y - 4

We can quickly get a temporary value for x by altering the original equation.

x - y = 15

Add y to both sides.

x = 15 + y

Now that we have a value of x, we can find the exact value of y.

2 (15 + y) + 8 = 3y - 4

Distributive property.

30 + 2y + 8 = 3y - 4

Combine like terms.

38 + 2y = 3y - 4

Subtract 2y from both sides.

38 = y - 4

Add 4 to both sides.

y = 42

Now that we know the exact value of y, we can plug it back into the original equation.

x - 42 = 15

Add 42 to both sides.

x = 57