Question

A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation?

Answer 1

Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

$y=2(x+3)$

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

$y=3x+5$

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

$y=2(x+3)\\y=2x+6\\-2x+y=6$

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

$-2x+y=6\\2x-y=-6$

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

$y=3x+5\\-3x+y=5\\3x-y=-5$

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.