Write a system of equations for the problem: The sum of two numbers is 33. The larger number is 3 more than two times the smaller number. What are the numbers?

Question

Identify the variables and write a system of equations for the story problem.

Answer 1

Step 1, label variables.

x=larger number

y=smaller number

 

Step 2, Convert sentences into equations

The sum of 2 numbers is 33.

x + y = 33

The larger number (x) is 3 more than 2 times the smaller number (y)

x = 2y + 3

 

Step 3: Substitute second equation into first equation and solve for y.

 

(2y + 3) + y = 33

3y + 3 -3 = 33 -3

3y/3 = 30/3

y = 10

 

Step 4: Substitute solved value for y and solve for x

x = 2y + 3

x = 2(10) + 3

x = 20 + 3 = 23

 

Step 5: Check x+y=33, 23 + 10 = 33 Check.

Answer 2

Hi Lisa;

smaller...x

larger...2x+3

(x)+(2x+3)=33

x+2x+3=33

3x+3=33

Let's subtract 3 from both sides...

-3+3x+3=33-3

3x=30

Let's divide both sides by 3...

(3x)/3=30/3

x=10...smaller

2x+3=[(2)(10)]+3=20+3=23...larger

Let's check our work...

10+23=33