Question

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.

Answer 1

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

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

x - y = 15

2x + 8 = 3y - 4

Using the first equation, we can get an approximate value for x.

x = 15 + y

Now that we have a value for x, we can replace it in the second equation to find the 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 have the value of y, we can find the value of x.

x - 42 = 15

Add 42 to both sides.

x = 57