Question

a mason is a person who builds structures with bricks, stone, cement block, or tile. a mason usually uses mortar to hold the bricks together. a general rule of thumb in masonry is that $2\frac{1}{2}$ bags of mortar are needed for every 100 cement blocks. use a double number line to determine each answer. bags of mortar: 0, $2\frac{1}{2}$, 5, $7\frac{1}{2}$... cement bricks: 0, 100, 200, 300... (c) with $12\frac{1}{2}$ bags of mortar, how many blocks can the mason lay?

Explanation:

Step1: Find the rate of blocks per mortar bag

From the double number line, \(2\frac{1}{2}\) bags of mortar correspond to 100 blocks. So the rate is \(\frac{100}{2\frac{1}{2}}\) blocks per bag. First, convert \(2\frac{1}{2}\) to an improper fraction: \(2\frac{1}{2}=\frac{5}{2}\). Then, \(\frac{100}{\frac{5}{2}} = 100\times\frac{2}{5}=40\) blocks per bag.

Step2: Calculate blocks for \(12\frac{1}{2}\) bags

Convert \(12\frac{1}{2}\) to an improper fraction: \(12\frac{1}{2}=\frac{25}{2}\). Multiply the rate by the number of bags: \(40\times\frac{25}{2}\). Simplify: \(40\div2 = 20\), \(20\times25 = 500\).

Answer:

500