The difference between two numbers is 67. Four times the smaller is equal to 5 more than the larger. What are the numbers?

Question

The difference between two numbers is 67. Four times the smaller is equal to 5 more than the larger. What are the numbers?

Answer 1

Hi Alicia, 

Step One: Create our Let Statements

Let x= the smaller number 

Let y= the larger number

Step Two: Translate the sentences into an equation

The difference between two numbers is 67: y-x=67

Four times the smaller is equal to 5 more than the larger: 4x=5+y

Step Three: Solve the system of equations:

y-x=67 and 4x=5+y rewritten to cancel the y terms are -x=67-y and 4x=5+y

Adding these equations, we get:

-x+4x=67+5 Combine Like Terms

3x=72 Divide both sides by three

x=24

∴The numbers are 24 and 91 because 91-24=67.                                   

Best, 

Star

Answer 2

say L is the larger and S is the smaller

S + 67 = L (we would need to add to the smaller to get to the larger)
4S = L + 5 (simply writing down the second sentence)

Since we know L = S + 67 we can substitute (S + 67) instead of L in the second equation

4S = S + 67 + 5
3S = 72
S = 24
L = 91 (by simply adding 67)