Question

Word Problem " I need help solving this problem using quadratic equations.I need to show all work, If I can get step by step understanding I can then possibly start to solve the others on my own.

Answer 1

From the present question we will need to find the greatest common divisor between 144, 90, and 36 because the greatest common divisor will be the largest number of backpacks they can pack with numbers of pencils, note pads, and granola bars evenly.

From this information, to find the greatest common divisor, we must factorize the numbers. It means to write them as multiplication of prime numbers, as follows:

`\begin{gathered} 144=2*2*2*2*3*3=2^4*3^2 \\ 90=2*3*3*5=2^1*3^2*5^1 \\ 36=2*2*3*3=2^2*3^2 \end{gathered}`

From this, we can see that all of the numbers have in their factorization the number 2 at least once, and the number 3 at least twice. From this, we know that they can be rewritten as follows:

`\begin{gathered} 144=(2*3^2)*2^3=18*2^3 \\ 90=(2*3^2)*5^1=18*5^1 \\ 36=(2*3^2)*2^1=18*2^1 \end{gathered}`

It means that the greatest common divisor is 18, and from this, the largest backpacks they will be able to pack will be 18.