Question

The sum of two consecutive numbers is 77. the difference of half of the smaller number and one-third of the larger number is 6. if x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers?

Answer 1

2x+1=77
1/2x-1/3Y=6

These are the two equations

Answer 2

`x+y=77...(1)`

`(x)/(2)-(y)/(3)=6...(2)`

Explanation:

Let x is the smaller number and y is the larger number.

We have been given that the sum of two consecutive numbers is 77. We can represent this information is an equation as:

`x+y=77...(1)`

Half the smaller number:
`(x)/(2)`,

One-third of the larger number:
`(y)/(3)`

The difference of half of the smaller number and one-third of the larger number is 6. We can represent this information is an equation as:

`(x)/(2)-(y)/(3)=6...(2)`

Therefore, our required equations are:

`x+y=77...(1)`

`(x)/(2)-(y)/(3)=6...(2)`