Question

1. a printer is packaging books in identical boxes. she has filled seven boxes and all but 5 books in another box. she has packed 51 books. how many books are in a full box? solve. draw a picture for this problem.

Explanation:

Step1: Set up the equation

Let \(x\) be the number of books in a full box. The total number of books is \(7x+(x - 5)\). We know the total number of books is 51. So the equation is \(7x+(x - 5)=51\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+x-5=(7 + 1)x-5=8x-5\). So the equation becomes \(8x-5 = 51\).

Step3: Isolate the variable term

Add 5 to both sides of the equation: \(8x-5+5=51 + 5\), which simplifies to \(8x=56\).

Step4: Solve for \(x\)

Divide both sides of the equation by 8: \(x=\frac{56}{8}\).

Answer:

6

For the picture:

• Draw 7 rectangles (to represent the 7 full boxes).
• Draw one more rectangle (to represent the 8th box). Inside this 8th rectangle, draw a smaller circle or a part - filled region to indicate that it is missing 5 books compared to a full box. And write the number 51 near the group of boxes.