Question

1.Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation?
2.

Answer 1

1. The answer for #1 is:

Equation 1: 2y+x=5

Equation 2: 5x-y=3

Answer 2

Answer: 1. 2y+x=5, 5x-y=3 or y-5x=3 and 2. y=x-3 or y=3-x, y=1/3(x+9)

Explanation:

In first question, x represent the smaller number and y represent the larger number.

And, Twice a number added to a smaller number is 5.

That is, 2×larger number + smaller number = 5

⇒2y+x=5,

Moreover, The difference of 5 times the smaller number and the larger number is 3.

that is, 5× smaller - larger = 3 or larger - 5× smaller = 3

⇒ 5x - y =3 or y - 5x =3

In second question,

y represents the smaller number and x represents larger number.

And, A number, y, is equal to the difference of a larger number and 3.

That is, y= x -3 or y= 3- x

Moreover, The same number is one-third of the sum of the larger number and 9.

⇒ y = 1/3(x+9)