Algebra Problem

Question

The sum of two numbers is 30. The difference between 1/2 of one of the numbers and 1/3 of the other is 5. Find the two numbers.

Answer 1

Let x = the first number and y = the second number

"The sum of two numbers is 30." translates into

x + y = 30...............(1)

"The difference between 1/2 of one number and 1/3 of the other is 5" translates into

1/2 x - 1/3 y = 5......(2)

Before we solve, let's take equation (2) and multiply everything through by 6, so that we can get rid of the fractions:

6(1/2x - 1/3 y) = (5)6

3x - 2y = 30..........(3)

We now use systems to solve for x and y. Using equations (1) and (3)

2(x + y = 30) ----------->2x + 2y = 60.....(a)

3x - 2y = 30-------------->3x - 2y = 30.....(b)

Adding (a) and (b) together we get

5x = 90

x = 18

Which means that by equation (1) 18 + y = 30 ----> so y = 12.

Thus our two numbers are 18 and 12.

Hope this helps

Mr. K

Answer 2

x + y = 30

x/2 - y/3 = 5

x + y = 30

3x - 2y = 30

2x + 2y = 60

3x - 2y = 30

5x = 90

x = 18

What is the value of y?

Answer 3

2 unknowns, so you need 2 equations.

From the 1st sentence: X + Y = 30

From the 2nd sentence: X/2 - Y/3 = 5

There are 2 ways to solve this pair of equations:

1. Use the expression for X or Y from the first equation. In the second equation, substituite the expression (for either X or Y) and you will now have an equation with just 1 unknown.
2. Multiply the 2nd equation by either 2 or 3. This will give an X or Y term that matches the first equation. Now you can subtract the equation to eliminate an unknown.