Please help me in solving these questions on College Algebra

Question

We have an assignment on our Algebra and I'm having a hard time on solving these questions. Can you guys help me answer this one. Please also do provide some solutions for me to get a gist of it. Thank you Wyzanters! :)

Two-Variable Linear Equations Problems

Read and understand the problem. Make an accurate graph (as possible) to show the system
of lines and then SOLVE the system.

Here are the questions:

1. Ethan and Nathan work in retail, in different shops. Ethan makes $280 per hour plus $160 for
each item she sells, and Nathan makes $400 per hour plus $120 for each item she sells. Dianne
makes $480 per hour plus $80 for each item she sells, but Dianne isn't even a part of this word
problem, so don't need to worry about that. In fact, we're not even sure why we bombarded you with
that extraneous information. We just thought you might like to know what Dianne's up to.
How many items would each boy need to sell in one hour in order for Ethan and Nathan to make the
same amount of money during that hour?

2. Loren and Marisol each bought cookies on Sunday and started eating their cookies the next day.
They are trying to eat as many of them as possible before they need to give cookies up entirely for
Lent.
Loren took 6 days to eat 30 cookies, while Marisol took 8 days to eat 24 cookies. On what day of the
week did they have the same number of cookies still left to be eaten? Hint: it was the day they both
had to be rushed to the local ER to have their stomachs pumped.

3. Lois and Joseph start saving pennies on New Year's Day. Lois has 5 pennies and saves 6
pennies every day. Joseph starts with 4 pennies and saves 2 pennies every day. This situation is
actually kind of embarrassing, considering that both are in their thirties. Such is the life of an actor...
After how many days will they have the same number of pennies?

Answer 1

Paige, here we go:

 

1.  Let's think about how you would figure this out in real life and put it into an equation.  If Ethan sells 2 items in one hour, he makes $280 + $160(2), so he makes $600, right?  If we want to know how much he makes for x items, then we say 280 + 160x = "something"  Can you figure out the same for Nathan?

 

Now, they both have to make the same, according to the problem.  Remember that if a + b = "something" and d + e = "something", then a +b = d + e.

 

Set up your two equations. Since they both have to equal the same, set the left sides equal to each other and solve for x.  Your answer should be x = 3.

 

2. Loren and Marisol sure are hungry!  If Loren eats 5 cookies a day, how many cookies does she have left after 3 days?  She's eaten 15, so she has 15 cookies left.  30 - 5(3) = 15. After x days, we'd have 30 - 6x.

 

What is the equation for Marisol?  Again, since the right side of both equations are the same, according to the problem, we set the left sides equal to each other and solve for x.  Your answer is  Wednesday.

 

3. This is pretty much like #1, except that there is no answer. See if you can figure out why.