One number is 4 more than another. Four times the smaller is equal to 3 times the larger increased by 1. Find the numbers

Question

this is a very important question, i have no clue how to do this

Answer 1

We know there are two numbers, one smaller than the other. Let's call the smaller number x, and the larger number y.

 

Now let's translate each statement into an equation.

 

"One number is 4 more than another."

This means the larger number is 4 more than the smaller number. We can represent that as:

x + 4 = y

 

"Four times the smaller is equal to 3 times the larger increased by 1."

Since we know the smaller number is x, the left side of this equation is 4x. For the right side of the equation, we have 3y increased by 1, which is 3y+1. Putting this together:

4x = 3y + 1

 

Now we have a system of 2 equations to solve:

x + 4 = y

4x = 3y + 1

 

We can first solve for x by plugging in the first equation into the second equation:

4x = 3(x + 4) + 1

4x = 3x + 12 + 1

4x = 3x + 13

x = 13

 

Now we can plug x = 13 back into x + 4 = y:

(13) + 4 = y

17 = y

 

So the final answer is:

x = 13

y = 17

Answer 2

Hello Ashley,

 

To solve the problem, write the following system of 2 linear equations corresponding to the definition:

x = y + 4

3x + 1 = 4y

 

Re-write it in canonical form:

x - y = 4
3x - 4y = -1

Next, solving this system of linear equations either manually, or using online System of Linear Equations Solver (http://examn8.com/SystemOfEquations.aspx) gives the answer:

x = 17 (the larger number)
y = 13 (the smaller number)

 

Note: to solve the System of Linear Equations I recommend to use the most universal and computationally-efficient method shown below:

 

Systen of 2 Linear Equations with 2 unknown variables X and Y in canonical form:

A₁X+B₁Y=C₁
A₂X+B₂Y=C₂

The Solution:

First, calculate the determinant:

 

determinant = A₁*B₂-A₂*B₁

 

Find X and Y directly provided that determinant is not 0 (otherwise, there is no valid solution for X and Y):

X = (B₂*C₁-B₁*C₂) / determinant
Y = (A₁*C₂-A₂*C₁) / determinant

 

Hope this will help.