Question

two numbers total 33 and have a difference of 5. Find the two numbers.

Answer 1

The larger number is ___ and the smaller number is__

Answer 2

Well, let's call the two numbers x and y. One of them must be greater than the other if their difference is 5 so let's let the bigger one be x.

Then we know that x + y is equal to 33 and the difference is positive so it's the bigger one minus the smaller one or x - y so that x - y = 5

So now we have

x + y = 33 and x - y = 5

Do you know where to go from here?

Answer 3

no

Answer 4

Do you know how to manipulate equations like if a - b = 10 then a = 10 + b?

Answer 5

Well each operation in arithmetic has it's opposite. The opposite of addition is subtraction, the opposite of multiplication is division;

so when you have things on different sides of the equal sign you can put them on the other side by doing the opposite operation on each side.

For example,

a + b = 12

if we want to move b to the opposite side we put the opposite of b on each side, or -b

a + b - b = 12 - b

but

b - b = 0

so we're left with a = 12 - b

Which makes sense if you think if a and b add together to get 12, then 12 minus b should be a

7 + 5 = 12

12 - 7 = 5

In the above problem we have

x + y = 33

and x - y = 5

so that x is 5 larger than y or

x = y + 5

Now we can just replace the x in

x + y = 33

with y + 5 because they are the same thing

so now we have

y + 5 + y = 33

or

2y + 5 = 33

Do you know what you could do from here?