Question

A rectangular crate of bottles holds 72 bottles. The rows across the width of the crate hold 1 bottle less than the rows across the length of the crate.

How many bottles are there in the longer rows?
Write an equation where b is the number of bottles in the longer rows that can be used to solve this problem.

Answer 1

The equation is:

72 = (b - 1)*b = b^2 - b

And the solution to this problem is:

b = 9

So we have 9 bottles in each one of the longer rows.

Explanation:

Let's use the variables:

b = number of bottles in the longer rows

a = number of bottles in the shorter rows.

We know that the total number of bottles in the crate will be equal to the product between a and b.

then:

72 = a*b

And we also know that

"e rows across the width of the crate hold 1 bottle less than the rows across the length of the crate."

This means that

a = b - 1

Now, we could replace this in the above equation to get:

72 = (b - 1)*b = b^2 - b

Then we have the quadratic equation:

b^2 - b - 72 = 0

The solutions of this equation can be found if we use Bhaskara's formula, the two solutions are:

`b = (1 +- √((-1)^2 - 4*1*(-72)) )/(2*1) = (1 +- 17)/(2)`

Then we have two solutions:

b = (1 - 17)/2 = -16/2 = -8 (this is a negative number, and has no meaning in our case, then this solution can be discarded)

the other solution is:

b = (1 + 17)/2 = 18/2 = 9

This is our solution, the larger rows have 9 bottles each.