Lara S. answered • 10/08/14
Tutor
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STEM Specialist and Math Coach with Teaching Experience
To set this up, let's start by making up some shorthand. Lets say "R" is the number of rulers.
With word problems, we have to make sure we Know what the question is ASKING AND what it is TELLING us.
Now, the question is ASKING:what conditions is the store less expensive? Basically, how many rulers can I buy so that it costs LESS to buy them at the store.
They TELL us: At an online store, rulers cost $.89 cents plus $5 for shipping. At a local store, rulers cost $.95 cents
Now we need to translate this information into an equation (this does take some practice).
Total amount at an Online store will be $.89 times the number of rulers "R" plus the $5 shipping charge.
Total amount at an Online store: 0.89R+5
Total amount at an Local Store will be $.95 times the number of rulers "R"
Total amount at an Local store: 0.95R
Total amount at an Local store: 0.95R
Again we want to know how many rulers can I buy so that it costs LESS to buy them at the store.
This will be a an inequality
0.95R<0.89R+5
Solving for R
0.95R-0.89R<+5
0.06R<5
R<5/(0.06)
R<83.333
So if I buy 83 rulers or less, it is cheaper at the local store.
Second Part
If there is free shipping on online orders over $50, how does your answer change?
what it is really asking: How many ruler do I need to buy to so theat the total is over $50 (for free shipping)?
Now how many can I buy locally so it is still cheaper?
0.89R+5>50
0.89R>45
R>50.56
I must buy 51(or more) rulers so it will cost more than $50
The previous answer still applies for less than 51 rulers (because there is still a shipping fee) but if we buy 51 (or more) rulers, it is cheaper online (because no shipping fee and each ruler is cheaper)
Comment if you need clarification on anything.
