One band has fewer than 40 speakers. They stack them in an array exactly 9 high. How many speakers could they have? Explain how you know.
9 * 4 = 36 < 40
To find the number of speakers the band could have, we need to divide the total number of speakers by the number of speakers stacked in each array.
Given that the band has less than 40 speakers and they stack them exactly 9 high, we can assume that the number of speakers is a multiple of 9.
To find the maximum possible number of speakers, we can divide 40 by 9 (the maximum possible stacking height). So, the band could have a maximum of 4 arrays, each containing 9 speakers.
Therefore, the maximum number of speakers the band could have is 4 arrays multiplied by 9 speakers per array, which equals 36 speakers.
Since it's stated that the band has fewer than 40 speakers, the band could have any number of speakers between 1 and 36, as long as it's a multiple of 9.
To find out how many speakers the band could have, we need to divide the total number of speakers by the height of the array, which is 9.
If we let "x" represent the total number of speakers, then we have the equation:
x = 9 * y
Where "y" represents the number of arrays that can be formed.
Since we know the band has fewer than 40 speakers, we can set up an inequality to reflect this:
x < 40
To find the maximum number of speakers, we can substitute the value of "x" in the inequality:
9 * y < 40
Now, to solve for "y," we divide both sides of the inequality by 9:
y < 40 / 9
Dividing 40 by 9 gives us approximately 4.44. However, since "y" represents the total number of arrays, it should be a whole number. Therefore, "y" can be a maximum of 4.
Substituting the value of "y" back into the equation for "x," we get:
x = 9 * 4
x = 36
So, the band could have a maximum of 36 speakers.