The sum of two numbers is 6. Four times the larger number plus three times the smaller number is 38. Find the numbers.

Question

I need help on this word problem because I do not understand it at all. 

Answer 1

Hi Allie!

In order to answer this question, we need to write some equations.

Let's translate the question from words into numbers and variables.

 

"The sum of two numbers is 6" is the same thing as writing: x + y =6

 

"Four times the larger number plus three times the smaller number is 38" we can rewrite as:

4(the bigger number) + 3(the smaller number)=38

 

If we decide that x=the bigger number and y=the smaller number, we get:

4x + 3y=38

 

Now we have two variables and two equations, which is all we need to solve the problem.

Since x + y=6, we know that x=6-y

We can substitute (6-y) for x in our second equation, which gives us:

4(6-y) + 3y = 38

24-4y+ 3y = 38

-y=14

y=-14

 

Now let's solve for x:

4x + 3(-14)=38

4x + -42=38

4x=80

x=20

 

So our final answer is: x=20 and y=-14

 

I hope that helps you understand how to approach this type of problem!

Answer 2

You need to set up two equations.  First lets define the variables.  We will let A be the first or larger number and B be the second or smaller number.

 

a+b=6

4a+3b=38

 

Now solve for one of the variables in one of the equations.

Substitute that value in the other equation and solve for the variable.

 

Lets solve for a in the first equation a=6-b

 

Now, we'll substitute that in the second equation.

4(6-b)+3b=38 and multiply it out.

24-4b+3b=38 lets combine our like terms.

24-b=38  lets add b to both sides.

24=38+b lets subtract 38 from both sides.

-14=b

 

Now we will plug -14 in for B in the first equation

 

a+(-14)=6

We will solve for A

a=20.

 

Now, lets plug both answers in to the second equation to see if they are right.

4(20)+3(-14)=38

80+(-42)=38

38=38

 

The larger number is 20 and the smaller number is -14.