Question

A monument made of a certain number of rows consisting of cube-shaped bricks starts with a row of 34 bricks. The row above has 31 bricks, the row above that has 28 bricks, and so on, such that each row has three fewer bricks than the row below it. A portion of the monument is shown below. Later a student notices that the total number of bricks used in the monument is just enough to create the brick floor of a rectangular patio that is one layer of bricks, seven × as long as it is wide. (No bricks are broken to make the floor.) How many rows of bricks does the monument have?

a) 4
b) 5
c) 6
d) 7

Answer 1

To find the number of rows of bricks in the monument, we need to determine the width and length of the rectangular patio created by the bricks and solve an equation.

Step-by-step explanation:

The monument has a pattern of rows in which each row has three fewer bricks than the row below it. The total number of bricks used in the monument is just enough to create a rectangular patio that is one layer of bricks and seven times as long as it is wide. To find the number of rows of bricks, we need to determine the width and length of the patio and then calculate the number of rows needed to form that shape.

Let's start by finding the width of the patio. We know that each row has three fewer bricks than the row below it. So, the difference in the number of bricks between two consecutive rows is 3. If we let x represent the number of rows, then the width of the patio can be represented as (34 - 3(x-1)).

Next, we need to find the length of the patio. Since the patio is seven times as long as it is wide, the length can be represented as 7 times the width: 7(34 - 3(x-1)).

Finally, the total number of bricks used in the monument is equal to the number of bricks needed to create the patio floor. The formula for the number of bricks needed to create a rectangular floor is width times length. So, we can set up the equation as: (34 - 3(x-1)) * 7(34 - 3(x-1)) = (the total number of bricks used in the monument).

To find the number of rows of bricks, we need to solve this equation. Once we determine the value of x, it will represent the number of rows in the monument.