I'm learning about "comparing linear functions word problem"
30 points!

heloïse considered two types of printers for her office. each printer needs some time to warm up before it starts printing at a constant rate.

the first printer takes 30 seconds to warm up, and then it prints 1 page per second.

the printing duration (in seconds) of the second printer as a function of the number of pages is given by the following table of values:

For the first part of the problem we want to know what printer takes more time to warm up. The first printer takes 30 seconds but what the second printer?

If we look at the table and make some more entries, we can solve it.

In forty seconds the second printer can print 16 pages. In sixty seconds it prints 32 pages. The difference between the number of pages is 16. The difference between the amount of time is 20. Why not work backwards to 0 pages and see what the time is?

We know that the line is linear which means the slope is constant.

16 pages - 16 | 40 seconds - 20
0 pages | 20 seconds

So, the first printer takes longer to warm up.

Now for the second part of the question.

The first printer can print 1 page per second. But because the printer took 30 seconds to warm up, we need to subtract 30 seconds from 100 seconds.

100 - 30 = 70

So, the first printer can print 70 pages in 100 seconds.

For the table, it's even easier. We know the difference between the pages and time amounts are 16 and 20 respectively.

Just add another entry to the table.

Add 16 pages to the last entry in the table. Likewise with the 20 seconds.

48 pages + 16 | 80 seconds + 20 seconds

64 pages | 100 seconds

So, first the printer prints more pages in 100 seconds.

1.17+3.99a. you combine the terms with a to create 3.99 and the 1.17 stays because it has no like terms or a variable