The some of two numbers is 80 and the greater number exceeds twice the smaller by 11. Find the number

Question

Maths , cannot solve problems like this and algebra also I have been working on it but it's not easy

Answer 1

Hi Tabish,

 

The n and m be your numbers. The sum of the numbers is 80, so m + n = 80.

 

Let m is the greater number. It exceeds twice the smaller number, n, by 11. m = 2n + 11

 

So, we have two equations and two unknowns:

 

m + n = 80

m = 2n + 11

 

or, we can rewrite the second equation

 

m + n = 80

m -2n = 11

 

Multiply through the top equation by 2.

 

2m + 2n = 160

m -2n = 11

 

Now add the two equations, which will eliminate n.

 

3m = 171

 

or

 

m = 57

 

We can now use one of the original equations and solve for n knowing this value of m. Let's use the first equation m + n = 80.

 

n = 80 - m

 

or

 

n = 80 - 57 = 23

 

So, m = 57 and n = 23