Question

There are two numbers. the sum of the larger number and three times the smaller number is 14. the larger number is two more than the smaller number. what is the larger number?

A. 2
B. 3
C. 4
D. 5

Answer 1

To find the larger number, we can set up equations based on the given information and solve them simultaneously. The larger number is 5.

Step-by-step explanation:

To solve this problem, let's assign variables to represent the larger and smaller numbers. Let's call the larger number 'x' and the smaller number 'y'.

From the given information, we can write the following equations:

x + 3y = 14

x = y + 2

We can solve these equations simultaneously to find the values of 'x' and 'y'.

Substituting the value of 'x' from the second equation into the first equation, we get:

(y + 2) + 3y = 14

Expanding and simplifying:

4y + 2 = 14

Subtracting 2 from both sides:

4y = 12

Dividing both sides by 4:

y = 3

Substituting y = 3 in the second equation to find x:

x = 3 + 2 = 5

Therefore, the larger number is 5. So, the answer is D. 5.

Answer 2

First, you have to give each a variable. In this case, the smaller number will be x and the larger number will be y.

Next, you need to make the equations. Your equations are:
y+3x=14
x+2=y

What you're solving for is y because the questions asks what the larger number is.

Then, substitute. It will be this after substituted:

x+2+3x=14

Combine like terms.

4x+2=14

Subtract by 2 on both sides.

4x=12

Divide by 4 on both sides.

x=3

^This what your smaller number is but you can easily find what y (the larger number) is. Substitute x into the other equation, which is basically adding 2 to 3.

y=5

(D)