How would I write this out ?

Question

One number is five less than another. Their sum is eleven. Find both numbers.

Answer 1

One number is five less than another. Their sum is eleven. Find both numbers.

Let x be the first number for example. Then y, a second number, could be represented by this equation:

y = x - 5 This represents the first statement. Next

x + y = 11 This equation represents ‘their sum is eleven’.

Now we can solve the system of equations using substitution since we already have an expression equal to one of our variables, y. Use x - 5 from the first equation and substitute for y in the second equation. This gives:

x + x - 5 = 11 Combine like terms to get:

2x - 5 = 11 Add five to both sides of the equation:

2x = 16 Divide by 2 to solve for x:

x = 8 Now given that x equals 8 and the sum

of x and y is 11, 11 minus 8 gives 3. Thus:

y = 3

The two numbers are 3 and 8. Check back into the words to make sure that the answer makes sense. Is one of the numbers five less than the other?

8 - 3 = 5 Yes.

Is their sum eleven?

3 + 8 = 11 Yes.

Hope this helps!

~Jes

Answer 2

It is a question of translating the words into equations that you can solve.

Let's say the first number is x and the second is y:

1. One number is five less than another MEANS x=y-5
2. Their sum is eleven MEANS x+y=11

The next step is to CONVERT the first equation into an easier form to work with: x=y-5 is the same as x-y=-5

Then ADD those two equations together (up and down style might make more sense):

x - y = -5

x + y= 11

---------

x+x-y+y=-5+11 SIMPLIFIES to 2x=6

SOLVE 2x=6 {x=3}

REPLACE the variable x with its actual value in x+y=11 and SOLVE for y {3+y=11 or y=8}

check your work: 3 is 5 less than 8 and 3 plus 8 equals 11