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Getting from point a to point b: Hattie purchases 3 books for $3.75 each 5 notepads for $1.75 each. She uses the following equation to figure the total (before tax): (3 x $3.75) + (5 x $1.75) Which of the following is another that could also be used? a. (3 x 5) + ($ 3.75 x $1.75) b. (3 + 5) + ($3.75 x $1.75) c. (8 x $3.75) - $10 d. 15 + ($3.75 x $1.75) e. $3.75 + $1.75 I know that the correct answer is c just by doing the calculation, what I want to know is how is this equation derived from the data given; what principle(s) are used to come up with (8 x $3.75) - $10?

Mathematics
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note that $3.75 is exactly $2 more than $1.75 so, for every one of the 5 x $1.75, you can move $3.75 into the $3.75 count as longas you reduce the 5 x cost by $2
I hope that made sense?

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Other answers:

(3 x $3.75) + (5 x $1.75) = (3 x $3.75) + (5 x ($3.75 - $2.00))
http://i1.kym-cdn.com/entries/icons/original/000/009/993/tumblr_m0wb2xz9Yh1r08e3p.jpg
lol! ^^
@jagatuba - did I explain it clearly enough for you?
No I'm sorry. I still cannot see how we are getting from (3 x $3.75) + (5 x $1.75) to (8 x $3.75) - $10 nor what if any mathematical principles are involved.
brb
ok, do you agree with this step? (3 x $3.75) + (5 x $1.75) = (3 x $3.75) + (5 x ($3.75 - $2.00))
I don't believe there is any deep mathematical principal being used here - just re-arrangement of monetary amounts to make the calculation easier.
you basically need to have noticed that $3.75 is exactly $2 more than $1.75 and that 5 x $2 is a nice easy calculation
you will usually find street merchants are very good at these types of calculations. :)
I see thank you for the explanation @asnaseer. Sorry it took so long for me to respond back. I was just getting off work and then went Christmas shopping.
np, and yw :)

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