Algebra is a tool. Practice helps us learn how to use it. Here are some ways to practice Algebra in ordinary activities.
"How much is this with the discount?"
You are shopping at Penney's. The sign on a rack says, "St. Johns Bay Tops 40% Off Marked Price." Your sister looks at a top and asks, "How much is this with the discount?" You want a way to figure the sale price no matter the marked (original) price or the discount rate.
What do you want to find? The sale price. Let's label that s.
What is the marked price? Let's label that p.
What is the discount? Let's label that d.
So now, how do we use the discount to find the sale price from the marked price?
s = ?
s = p - d
We have to remember that the discount rate is a percentage of p. Let's label that r. We also want to simplify the arithmetic, make it easier if we are figuring this in our heads in the store. We know that p equals 100% of itself. And we are subtracting a smaller percentage, the discount rate, which is r. So what is left is (100 - r)%, or (100 - r)% of p, which is p(100 - r).
We know that x% of n = xn/100, for instance, 20% of $50 = 20*$50/100 = 2*$50/10 = $100/10 = $10.
So s = p(100 - r)/100.
Now back to Penney's. You ask your sister, "What is the marked price?" She says, "$34.99." We want to make this easier, so first we add one cent to round the price to $35. We'll take that cent back off at the end. And we're taking 40% off.
p = 35
r = 40
s = p(100 - r)/100 = $35(100 - 40)/100 = $35*60/100 = $35*6/10 = $210/10 = $21.
Now we take the added cent off: $21.00 - $0.01 = $20.99.
You answer your sister, "That will be twenty dollars and ninety-nine cents."
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