Two numbers have a sum of 24, and 7 times the first number minus the second number is equal to 16. What is the smallest number?

Question

I'm supposed to translate the word problem into a system of equations then solve. Please help!!

Answer 1

Let x and y be the 2 numbers.

 

Solve this system of equations:

 

x + y = 24

7x - y = 16

 

Add the 2 equations and get

 

8x = 40

x = 40/8 = 5

 

y = 24 - 5 = 19

 

The 2 numbers are 5 and 19.  Test the answers.

 

 

Answer 2

Hi Niya,

 

Let's call the two numbers A and B. 

 

Now, lets' read the problem word for word and convert it to math symbols:

"The sum of the numbers is 24" which means

 

A + B = 24  (This is the first equation of your system)

 

Next, we read, "7 times the first number minus the second number is equal to 16" which means

7A - B = 16  (This is the second equation of your system)

 

 

If I take the first equation and solve it for B (which means get B by itself on one side), we see that

B = 24 - A

 

Let's use this expression for B and substitute it in for B in the second equation

7A - B = 16

7A - (24 - A) = 16     See the replacement!  :)

 

7A - 24 + A = 16      Distribute the negative on the left side)

 

8A - 24 = 16

 

8A = 16 + 24

 

8A = 40

 

A = 5

 

which means that B must be 19 since the two numbers have to add up to 24.

 

A is the smallest number!  A = 5

 

Hope this helps!  :)