Question

Gabriela is building a brick wall. Each row of bricks is 6.5\,\text{cm}6.5cm6, point, 5, start text, c, m, end text tall except that the top row is 1\,\text{cm}1cm1, start text, c, m, end text shorter because it has no mortar. She wants the wall to be 259\,\text{cm}259cm259, start text, c, m, end text tall. Which equation can we use to determine rrr, the number of rows of bricks Gabriela needs in her wall?

Answer 1

Given :   Gabriela is building a brick wall Each row of bricks is 6.5 cm except that the top row which  is 1cm shorter  

To find :   number of rows of bricks Gabriela needs in her wall

Solution:

Each Row Height = 6.5 cm

Last Row height = 6.5cm - 1 = 5 .5 cm

Total Height = 259 cm

Let say number of Rows = R

=> 6.5 ( R - 1) + 5.5  = 259

=> 6.5R - 6.5 + 5.5 = 259

=> 6.5R  - 1 = 259

=> 6.5R = 260

=> R = 260/6.5

=> R = 40

Total Number of Rows  =  40  

Expressions can be used

= > 6.5 ( R - 1) + 5.5  = 259  ,  6.5R  - 1 = 259

Each Rows height * number of Rows - ( height shorter of last low) = Total Height

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Answer 2

Options:

A.) 6.5 ( r - 1 ) = 259

B.) 6.5r - 1 = 259

C.) 6.5r - r = 259

D.) 6.5 ( r - 1 ) + 1 = 259

Answer:

The answer is:

B.) 6.5r - 1

Step-by-step explanation:

We know we want to reach a height of 259 cm. Let's consider the height of the wall with each row of bricks. Each row increases the height by 6.5 cm.

                                                                                                             

Row                                   Height

1 (top row)                         6.5 - 1

2                                        6.5 - 1 + 6.5

3                                        6.5 - 1 + 6.5 + 6.5

. . .                                      

r                                         ?

                                                                                                             

What's the pattern?

We can rewrite the repeated addition using multiplication.

                                                                                                             

Row                       Height                       Expression

1 (top row)             6.5 - 1                         6.5 ⋅ 1 - 1

2                            6.5 - 1 + 6.5                6.5 ⋅ 2 − 1

3                            6.5 - 1 + 6.5 + 65        6.5 ⋅ 3 − 1

. . .

r                       6r − 1                           6.5 ⋅ r − 1

                                                                                                             

So the wall is 6.5r - 1 cm tall when there are r rows of bricks.

Since r represents the number of rows Gabriela needs in her wall, and 6r - 1 represents the height of the wall when it has r rows, we can set up an equation to see how many rows it takes to reach a height of 259 cm.

height of the wall = 259

6.5r − 1​ = 259

We can use the equation 6.5r - 1 = 259 to determine r, the number of rows of bricks Gabriela needs in her wall.