Chapter 3.5, Problem 1G

Suppose that you have four people in your family, and you want to hang a picture of each family member. Aww, that’s sweet. Anyhow, the wall you choose is 60 inches wide, and each of the picture frames is 8 inches wide. To make everything look just right, you want to make the wall space between the edges of each frame identical, and put that same amount of space between the ends of the wall and the edge of the nearest frame. Each frame has a single hook in the center of its back. Where should you put the four nails needed to hang the pictures?

Step 1: Understand the problem.

a. Write down the relevant information provided by the problem.

What exactly are you being asked to find?

Step 2: Devise a plan.

When a problem describes something physical that can be drawn, a diagram is usually a good idea.

c. Draw a diagram based on the description of the problem including the relevant information you wrote down.

Based on your diagram, you should be able to note how much space will be covered by frames, and how many blank spaces there will be. Once you know that, you can find the total blank space and divide by the number of spaces to find how far from the edges of the wall the edge of each frame will be.

Step 3: Carry out the plan.

d. How much of the 60 inches will be covered by picture frames? How many empty spaces are there? What is it we’re trying to find? Give that quantity a variable name.

e. Note that the total 60 inches of the wall can be described by space covered by frames plus space in between frames. Use this idea to write and solve an equation that finds the space between frames. Then use that to describe the locations of all four nails.

Step 4: Check your answer.

f. Use your diagram to decide if the spots you found for the nails will work according to the statement of the problem.