Question

A printer takes 30 minutes to print a banner and a poster. I will take 50 minutes to print a banner and three posters. How long does it take to print a banner?

Answer 1

It takes the printer 20 minutes to print a banner

Explanation:

Notice that there are two unknowns in this problem: the time to print a poster and the time to print a banner. Let's assign the letter "b" to the time it takes to print a banner, and "p' the time it takes to print a poster.

So we can write the following two equations involving the total amount of time that takes to print in the two cases:

`b+p=30\\b+3p=50`

We can solve for the unknown "p" by subtracting term by term in the equation set above:

`b+3p=50\\b+p=30\\\\b-b+3p-p=50-30\\2p=20\\p=10`

So it takes 10 minutes to print each poster, we can find the time it takes to print the banner by using the value we just found in one of the equations:

`b+p=30\\b+10=30\\b=20`

So, it takes 20 minutes to print a banner.