Question

One number added to three times another number is 24. Five times the first number added to

three times the other number is 36. Find the numbers.

Answer 1

The first number is 3

The second number is 7

Explanation:

Let x = the first number

Let y = the second (other) number

One number added to three times another number is 24:

x + 3y = 24

Make 3y the subject by subtracting x from both sides: 3y = 24 - x

Five times the first number added to three times the other number is 36:

5x + 3y = 36

Substitute 3y = 24 - x into 5x + 3y = 36 and solve for x:

5x + (24 - x) = 36

5x + 24 - x = 36

Combine like terms: 4x + 24 = 36

Subtract 24 from both sides: 4x = 12

Divide both sides by 4: x = 3

Substitute found value of x into x + 3y = 24 to find y:

3 + 3y = 24

Subtract 3 from both sides: 3y = 21

Divide both sides by 3: y = 7