Makerspace Loans: Tables, Equations, and Graphs

Model how quantities change in a library makerspace.

Repair Kit Loans

Each repair kit contains 3 tools. Use x for the number of kits borrowed and y for the total number of tools borrowed.

A librarian chooses how many kits to lend. Which statement identifies the variables correctly?

A. The number of tools is independent; the number of kits is dependent.B. The number of kits is independent; the number of tools is dependent.C. The number of kits and the number of tools are both independent.D. The number of kits and the number of tools are both fixed.

Which equation gives the total number of tools borrowed?

A. y = x + 3B. y = x ÷ 3C. y = 3xD. x = 3y

Complete the missing value in the lending table.

Repair Kit Loans
Kits, x	Tools, y
0	0
2	6
5	?
8	24

When x = 5, y = tools.

Noor borrows repair kits containing a total of 21 tools. Every kit is complete.

How many kits does Noor borrow? kits

A graph places kits, x, on the horizontal axis and tools, y, on the vertical axis. Which point represents borrowing 4 kits?

A. (4, 12)B. (3, 12)C. (12, 4)D. (4, 7)

Chargers on the Shelf

The makerspace starts with 10 chargers. Each checkout lends 2 chargers, and none are returned during this period. Let x be the number of checkouts and y be the number of chargers left.

Which equation matches the charger graph?

A. y = 10 + 2xB. y = 2xC. y = 10 − xD. y = 10 − 2x

Use the charger graph. A librarian needs at least 4 chargers to remain on the shelf.

What is the greatest number of checkouts that can occur? checkouts

Eli says point C means that 6 checkouts have occurred and 2 chargers remain. Explain the error and state what point C actually means.

On another day, the makerspace starts with 14 chargers and still lends 2 per checkout. Which equation models this new situation using the same variable meanings?

A. y = 14 − 2xB. y = 14 + 2xC. y = 10 − 14xD. y = 2 − 14x

Packing Equipment Loans

A tool loan needs 2 labels for its case plus 1 label for each tool inside. Let x be the number of tools in a loan and y be the total number of labels needed.

10.

Which equation links the number of tools to the total number of labels?

A. y = 2xB. y = x + 2C. y = x − 2D. y = 2x + 1

11.

Complete the two missing entries.

Labels for Tool Loans
Tools, x	Labels, y
1	3
3	?
?	8
8	10

For 3 tools, the loan needs labels.
A loan that needs 8 labels contains tools.

12.

Graph the label relationship for loans containing 1, 3, 6, and 8 tools. Plot four points using the table. Do not connect the points.

13.

Sam has exactly 9 labels available for one tool loan. The loan still needs 2 labels for its case and 1 for each tool.

What is the greatest number of tools Sam can pack and label? tools