Please help me with my word problem.

Question

Shayla bought 18 books for $139. She paid $5 for paperbacks and $12 for hardback books. How many hardback books did she buy?

Answer 1

Let paperbacks be "p" and Hardbacks be "h".

Total number of books purchased is 18. So,

p+h = 18 ------------------ Equation 1

 

Now add value to the books. Cost of paperbacks is $5, hardbacks is $12 and total cost is $139.

5p + 12h = 139.

 

Now there are two equations and two variables.

 

Use the first equation to express one variable in terms of another.

p + h = 18 ----------- Subtract h on both sides to eliminate h on the left side.

p = 18-h -----------------Substitute p=18-h into second equation.

 

5p + 12h = 139

5 (18-h) + 12h = 139

90 - 5h + 12h = 139 ---------------- combine like terms 

90 + 7h = 139

90 -90 + 7h = 139 - 90 ------------------------Subtract 90 from both sides

7h = 49

7h/7 = 49/7 --------------------------------Divide both sides by 7

h = 7

 

Substitute h = 7 into first equation to find p.

 

p + h = 18

p + 7 = 18 -------------- Subtract 7 from both sides

p + 7 - 7 = 18 - 7

p = 11

 

Shayla purchased 11 paperbacks and 7 hardbacks.  

 

Varify your answer by substituting p = 11 and h = 7 into second equation.

5p + 12 h = 139

5 (11) + 12 (7) = 139

55 + 84 = 139

139 = 139