Question

One number is 2 times another number plus 3. Their sum is 21. Find the numbers. If x represents the smaller number, which of the following equations could be used to solve the problem? 2x + 3 = 21 3x + 3 = 21 3x + 6 = 21

Answer 1

Option 2nd is correct

`3x+3 = 21`

Explanation:

Here, x represents the smaller number.

As per the statement:

One number is 2 times another number plus 3. Their sum is 21.

"One number is 2 times another number plus 3" translated to

x = smaller number = another number

⇒
`\text{One number} = 2x+3`

It is also given that: Their sum is 21.

⇒
`\text{One number}+x = 21`

Substitute the given value we have;

`2x+3+x = 21`

Combine like terms:

`3x+3 = 21`

Therefore, the following equations could be used to solve the problem is,
`3x+3 = 21`

Answer 2

Let first number be x and the second number be y y = 2x + 3_______1 x + y = 21 y = 21 - x _______2 Substitute 2 into 1 21 - x = 2x + 3 Rearrange the equation ^ 2x + 3 = 21 - x 3x + 3 = 21 THEREFORE, The 2nd option out of the three is correct.