The sum of two numbers is 63 The smaller number is 21 less than the larger number. What are the numbers?

Question

I just need help with this problem any answer much appriecated

Answer 1

Let's call one number a and the other number b. The way to work this type of problem is to take the information you are given in words and turn it into math.

The sum of the two number is 63: a + b = 63

The smaller number is 23 less than the larger: a = b - 23

Since you cannot solve an equation with two variables (letters), use the second equation to change "a" into "b-23".

b - 23 + b = 63

Now you can solve for b. Combine like terms: 2b - 23 = 63

Add 23 to both sides: 2b = 86

Divide both sides by 2: b = 43

Now that you know what b is, you can plug it into either equation and solve for a: a + 43 = 63

Subtract 43 from both sides: a = 20.

Your two numbers are 20 and 43.

Answer 2

Let x be the larger number.

Then x-21 is the smaller number.

Add the numbers.

x+(x-21)=2x-21

Set equal to 63.

2x-21=63

Solve for x.

2x=84

x=42

42 is the larger number

x-21=42-21=21 is the smaller number