One number is six less than a second number. Four times the first is 15 more than 5 times the second. Find the numbers.

Question

Need the value of first and second number.

Answer 1

Quickly after reading the problem my mind thinks 2 variables I need to equations and luckily 2 were given!

 

So:

• let x be the first number
• let y be the second number

Then based on the first statement: x-6=y

Based on the second statement : 4x=5y+15

 

Now we have to combine the two equation to eliminate one of the variables.

 

Multiplying both sides of the first equation by 4 does not change the equality and gives you: 4x-24=4y

 

I want to get my constant terms all on the same side so in the second equation I subtract 15 from both sides to get:

4x-15=5y

 

Now I subtract the second equation from the first

 

  4x-24=4y

-(4x-15=5y)

distribute the minus sign

 

 4x -24 = 4y

-4x+15=-5y

 

combine

 

-9=-y or y=9

 

now all you have to is substitue 9 in for y in either equation;

so x-6=y becomes: x-6=9 so x=15