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 2½ bags of mortar are needed for every 100 cement blocks. use a double number line to determine each answer.
bags of mortar: 0, 2½, 5, 7½ (with a number line)
cement bricks: 0, 100, 200, 300 (with a number line)
how many bags of mortar will a mason need for 350 blocks?
options: 8 3/4, 7 1/2, 8 2/4, 8 1/2

Explanation:

Step1: Find the rate per 100 blocks

We know that for 100 cement blocks, we need \(2\frac{1}{2}\) bags of mortar. First, convert \(2\frac{1}{2}\) to an improper fraction or decimal. \(2\frac{1}{2}=\frac{5}{2} = 2.5\) bags per 100 blocks.

Step2: Determine the number of 100 - block units in 350 blocks

To find how many 100 - block units are in 350 blocks, we divide 350 by 100: \(\frac{350}{100}=3.5\)

Step3: Calculate the total bags of mortar

Since each 100 - block unit requires \(2.5\) bags of mortar, we multiply the number of units (3.5) by the bags per unit (2.5).
\(2.5\times3.5=\frac{5}{2}\times\frac{7}{2}=\frac{35}{4} = 8\frac{3}{4}\) (Wait, let's check using the double number line. The double number line has 0, 100, 200, 300 for blocks and 0, \(2\frac{1}{2}\), 5, \(7\frac{1}{2}\) for mortar. So from 300 to 350 is an additional 50 blocks, which is half of 100 blocks. So the mortar for 50 blocks would be half of \(2\frac{1}{2}\) bags. Half of \(2\frac{1}{2}\) is \(1\frac{1}{4}\) bags. Then for 300 blocks, we have \(7\frac{1}{2}\) bags. Adding the mortar for 50 blocks: \(7\frac{1}{2}+1\frac{1}{4}=7\frac{2}{4}+1\frac{1}{4}=8\frac{3}{4}\) bags.

Answer:

\(8\frac{3}{4}\) (which is the option "8 3/4")