How Do I Do This?

Question

The sum of two numbers is 66. The larger number is 8 more than the smaller number. What are the numbers?

Larger number:

Smaller number:

Answer 1

You have 2 unknown numbers and the problem gives you information for 2 equations. You can solve 2 unknown variables with 2 equations.

Define the variables:

x = smaller number

y = larger number

Use the wording of the problem to get your 2 equations:

sum of two numbers is 66 - in otherwords, if you add the 2 numbers together you get 66

x + y = 66

larger number is 8 more than the smaller number - this is a little harder - remember that you have to add 8 to the smaller number for it to equal the larger number

x + 8 = y

Now you can use substitution to solve for only one variable - plugging x + 8 for y into the 1st equation is easiest:

x + (x+8) = 66

x + x + 8 = 66

2x = 58

x = 29

Plug value of x into either equation:

29 + 8 = y

y = 37

You can then check the math and you will see that both added together is 66.

Larger number: 37

Smaller number: 29

Answer 2

I'm telling ya, when they first starting added letters into my math, it confused the heck out of me! Let's see what we can do.

Let a = the smaller number and b = the larger.

Sum is the result of addition.

a + b = 66

We turn the next sentence into an equation.

b = a + 8

Now, expressions on either side of the = can be swapped out (substituted) for each other since they are equal. We are going to replace b in the first equation with a + 8

a + (a +8) = 66

a + a + 8 = 66

Remember that a variable with no coefficient actually has a coefficient of 1 (a negative variable has a coefficient of -1), but it would be like calling me 1 David instead of just David.

2a + 8 = 66

2a + 8 - 8 = 66 - 8

2a = 58

2a/2 = 58/2

a = 29

b = a + 8

b = 29 + 8

b = 37

Larger number: 37

Smaller number: 29

Answer 3

x=smaller number

x+8=larger number

x+x+8=66

2x+8=66

2x=58

x=29

x+8=37

smaller number:29

larger number:37