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

Answer:

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

$\frac{x}{2}-\frac{y}{3}=6...(2)$

Step-by-step 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: $\frac{x}{2}$,

One-third of the larger  number: $\frac{y}{3}$

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:

$\frac{x}{2}-\frac{y}{3}=6...(2)$

Therefore, our required equations are:

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

$\frac{x}{2}-\frac{y}{3}=6...(2)$