Question

One number is 3 less than twice another. If their sum is 39, find the numbers.

Which of the following systems of equations represents the word problem?

y = 2x - 3 and y = x + 39
y = 2x - 3 and x + y = 39
y = 2(x - 3) and x + y = 39

Answer 1

Answer:
y = 2x- 3 and x + y = 39

Explanation:
Twice of a number indicates the 2x in the equation. It’s also 2 less than the 2x. That’s where the 2x-3 part comes from. The question indirectly states to find the sum of x and y. That sum should equal 39We can now plug in the information and get the second part of the equation, x+ y = 39

Answer 2

Answer with Step-by-step explanation:

Let x and y be two numbers.

One number is 3 less than twice another.

⇒ y=2x-3

Their sum is 39.

⇒ x+y=39

Hence, system of equations are:

y = 2x - 3 and x + y = 39

Putting y=2x-3 in x+y=39

x+2x-3=39

⇒ 3x-3=39

⇒ x-1=13 (dividing both sides by 3)

⇒ x=14

y=2x-3

⇒ y=2×14-3

⇒ y=28-3

⇒ y=25

Hence, Two numbers are:

14 and 25