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Question

The sum of two numbers is 55 The smaller number is 13 less than the larger number. What are the numbers?

Larger Number:

Smaller Number:

Answer 1

Let's let L be our larger number and S be our smaller number.

Since the sum of the two numbers is 55, we know that:

Equation (a): L + S = 55.

And since the smaller number is 13 less than the larger number, we know that:

Equation (b): S = L - 13.

Let's plug equation (b) into equation (a):

L + S = L + (L-13) = 55

This can be written as:

L + L - 13 = 2L - 13 = 55

Now let's add 13 to both sides:

2L - 13 + 13 = 55 + 13

So we have:

2L = 55 + 13 = 68

Dividing both sides by 2 gives us:

2L / 2 = L = 68 / 2 = 34.

So our larger number, L, is 34.

Let's go back to equation (a) and solve for S:

Equation (a): L + S = 55

34 + S = 55

34 + S - 34 = 55 - 34

S = 55 - 34 = 21

To double check our work, let's confirm that equation (b) is still satisfied:

S = L - 13 = 34 - 13 = 21, which confirms our previous solution.

So the larger number is 34 and the smaller number is 21.

Answer 2

x and x-13 are the numbers

x+x-13=55

2x-13=55

2x=68

x=34

x-13=21

21 nd 34 are the numbers