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# 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?

### 2 Answers by Expert Tutors

Arturo O. | Experienced College Instructor for Physics TutoringExperienced College Instructor for Physi...
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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.

Jim J. | Experienced Math/Science Teacher available to helpExperienced Math/Science Teacher availab...
5.0 5.0 (41 lesson ratings) (41)
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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!  :)