Question

Gabriela is building a brick wall. Each row of bricks is 6.5 cm tall except that the top row is 1 cm shorter because it has no mortar. She wants the wall to be 259 cm tall. Which equation can we use to determine r, the number of rows of bricks Gabriela needs in her wall?

Answer 1

Answer:

$6.5 r+5.5=259$.  

Step by step explanation:  

Let r be the number of rows of bricks Gabriela needs in her wall.

We have been given that each row of bricks is 6.5 cm tall. The top row is 1 cm shorter because it has no mortar. Gabriela wants the wall to be 259 cm tall.

The top row of wall be $6.5-1=5.5$ cm tall.

The length of wall will change with each row of bricks, therefore, 6.5*r will be height of wall with r rows.  

6.5*r+5.5 will be the height of wall Gabriela wants to make.

Now let us set an equation by equating height of r rows of 6.5 cm and top row of 5.5 cm with 259 cm.

$6.5 r+5.5=259$

Therefore, the required equation to find the number of rows of bricks Gabriela needs in her wall will be $6.5 r+5.5=259$.

Answer 2

Answer:  6.5 (r-1) + 5.5  = 259 or 6.5 r - 1 = 259

Step-by-step explanation:

Here, r represents the total number of rows.

According to the question each row is 6.5 cm tall.

And, the top row is 6.5 - 1 = 5.5 cm tall

Except this row total number of rows = (r-1)

Thus, the total length of these rows = 6.5 (r-1)

Hence, the total length of wall = total length of (r-1) row + total length of top row.

But Again according to the question,

The wall must be 259 cm tall.

⇒ 259 = 6.5(r-1) + 5.5

⇒ 6.5(r-1) + 5.5 = 259

⇒ 6.5 r - 6.5 + 5.5 = 259

⇒ 6.5 r - 1 = 259

Which is the required equation for finding the number of rows (r).