The difference between two numbers is 4. The sum of the smaller number and three times the larger number is 36. What are the two numbers?

Question

Solve the word problem using elimination. Set up a system of equations before solving.

Answer 1

x and y are two numbers, let x be the larger number

difference is 4

x - y = 4

sum of smaller and 3 times the larger is 36

3x + y = 36

add 2nd equation to the first

x - y = 4

3x + y = 36

4x = 40

x = 10

plug in 10 for x in 1st equation to find y

x - y = 4

10 - y = 4

y = 6

two numbers are 6 and 10

Answer 2

Hello, Ariana,

See the table below.

Let's call the two unknowns X and Y, and say that X is the smaller (line 1). Take the two statements in the problem and make them into equations (lines 2 and 3).

Rearrange line 2 so that we have an equation for Y (line 4). Use that value of Y in the line 3 equation, so that we get line 5. Now we have an equation with just X (line 6), so solve for X (lines 7 and 8). Use X = 6 in line 2 and find Y (line 9).

Finally, check to see if the values of 6 and 10 work [10-6=4? and 6+3(10)=36?]. Both work, so we are OK.

Bob