one number exceeds another by 18. The sums of the number is 62. What are the numbers

Question

my question is based on a math problem im having a hard time solving

Answer 1

Hello Destiny,

 

The way that I set up this problem is using the variables x and y.

 

1) You mentioned that one number exceeds another by 18, so we can represent use the following to represent it: 
y= x + 18.

 

2) The sum of the two numbers is 62. So we will have this: y + x + 18 = 62.

 

3) Now, let's go on to show the equation: y + x + 18 = 62.

When you subtract 18 from both sides, you will end up with y + x = 44.
Then you subtract x from both sides, and you will have y = 44 - x.

 

4) So we now have two equations: y = x +18 and y = 44 - x.

So we the two to be equal: x + 18 = 44 - x.
Add x to both sides, and subtract 18 from both sides. You will end up with 2x = 26. Divide by 2 on both sides, you will have x = 13.

 

So your final answer is y =31 and x = 13.

Answer 2

Destiny,

 

I wonder if you meant to type that the products of the 2 numbers is 62, otherwise, it is ambiguous.

 

You just need to convert the words into equations. If one number exceeds another by 18...

 

then this is put into equations  by

 

x= y + 18

where x "exceeds" y by 18,

 

then, if the product of the numbers is 62, then,

 

xy= 62

 

Can you combine these 2 equations and solve? For this case, a quadratic equation results and you will have to use the quadratic equation to solve.

 

 

 

 

Answer 3

You can guess and check....

Guess the smaller number is 20.  The larger number is 20 + 18 = 38. 

The sum of 20 and 38 is 58.  Pretty close to a sum of 62.

The two numbers need to be a little larger.  

Try the smaller number being 22.  The larger number is 22 + 18 = 40.

The sum of 22 and 40 is 62.   That works!  The numbers are 22 and 40.

 

You can use algebra.  Let 'x' be the smaller number and x + 18 be the larger number.  Their sum is 62, so...

x + x + 18 = 62

2x + 18 = 62

Subtract 18 from each side.

2x = 44

Divide each side by 2.

x = 22

x + 18 = 40

 

Hope it helps, Destiny.

Mary Ann