Word problem

Question

Harry is thinking of two numbers. The second number is 5 less than 3 times the first. Also 10 times the first number is 5 less than 5 times the second. What are the numbers? 

Answer 1

Assign variables for the number we want to find out.

 

 

Let the first number = x

Let the second number = y

 

 

Set up equation using the variables and info given.

 

y = 3x - 5           eq1

 

10x = 5y - 5        eq2

 

 

We have a system of equations.   We can substitute eq1 into eq2, so that eq2 is in terms of x.

 

10x = 5(3x - 5) - 5

 

 

We can now solve for x.

 

10x = 15x - 25 - 5

10x = 15x - 30

 

 

Subtract 15x on  both sides of equation.

 

-5x = -30

 

    x = 6

 

 

Substitute this value of x into eq1 to solve for y.

 

y = 3(6) - 5

y = 18 - 5

y = 13

 

 

We have now found our numbers.   The numbers are 6 and 13.