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

The first equation gives:

y = 2 * (x + 3) >>> y = 2x + 6

Or

2x - y = -6

The second sentence gives:

y = 5 + 3x >>> 3x - y = -5

The answer is (A), the first choice.

Answer 2

Let's say that the smaller number is x. That means that the first equation is y is equal to twice the sum of x and 3. Twice the sum of x and 3 (x + 3) is 2(x + 3). That means that the first equation is y = 2(x + 3). Simplifying, we get that y = 2x + 6. We can find the equation for this by subtracting 6 + y from each side. Doing that, we get 2x - y = -6. Now onto the second equation. The larger number (y) is equal to 5 more than 3 times the smaller number. 3 times the smaller number (x) is 3x. 5 more than that is 3x + 5. That means that y = 3x + 5. That means that 3x - y = -5. The choice that has these answers is the first choice, meaning that the answer is the first choice.