he bought 3 books the total was $150. one book cost 50% more Tham the total of the 2 other books. what's the cost of the more expensive book

Question

Helplease with the word problem listed thanks...........................................

Answer 1

x = cost of more expensive book

 

y = subtotal cost of the other books

 

x = 50% more than y, so x = 1.50y = 1.5y

 

x + y = total cost = $150

 

1.5y + y = 150

 

y = 150/2.5 = 60

 

x = 1.5y = 1.5(60) = 90

 

The more expensive book cost $90, the other two combined cost $60.

 

Answer 2

Let x = cost of one book

Let y = cost of 2nd book

Let z = cost of 3rd book

 

Using these variables, we can create equation based on the problem description.

 

x + y + z = 150    ------>  total cost of books                 eq1

 

x = y + z + 0.50     ------>  cost of one book compared to others            eq2

 

x - 0.50 = y + z      ------> rearranging  eq2

 

 

Now we can use the substitution method to solve for one of the variables.  Substitute eq2 into eq1.

 

x + (x - 0.50) = 150

 

 

Solve for x from this equation.

 

2x = 150.50

 

 

Divide both sides of the equation by 2.

 

x = 75.25

 

 

Substituting this value of x into eq2.

 

75.25 - 0.50 = y + z

 

74.75 = y + z

 

 

Based on this logic, y and z must be less than 74.75.  And neither of them cannot be 0 because each book has a cost.  Therefore, the most expensive book would cost $75.25