1. algebraic problem

1 The current price of a pair of basketball shoes is $30. The original price had been reduced by 25%. that reduced price was then lowered by 50% to arrive at the current price. What was the original price? In this last word problem it has a sign in it that i have no idea what it means and i also cant type it here for you to see but i'll try to explain it. It looks like a (cp) but just no space at all between the c and the p. Here is what the word problem is askin g me to do. 2. If (m cp n) = 1/m + 1/n + 1/m^2 + 1/n^2 for any values of m nd n, what is the value of ( 2 cp 4)? express your answer as a common fraction. 2. Originally Posted by xsriel 1 The current price of a pair of basketball shoes is$30. The original price had been reduced by 25%. that reduced price was then lowered by 50% to arrive at the current price. What was the original price?
Hello xsriel,

Find the original price (op)

${\color{red}op}-\underbrace{.25{\color{red}op}}_{\text{1st discount}}-\underbrace{.5({\color{red}op}-.25{\color{red}op})}_{\text{2nd discount}}=30$

${\color{red}op}-.25{\color{red}op}-.5{\color{red}op}+.125{\color{red}op}=30$

$.375{\color{red}op}=30$

${\color{red}op}=80$

Originally Posted by xsriel
In this last word problem it has a sign in it that i have no idea what it means and i also cant type it here for you to see but i'll try to explain it.

It looks like a (cp) but just no space at all between the c and the p.

Here is what the word problem is askin g me to do.

2. If (m cp n) = 1/m + 1/n + 1/m^2 + 1/n^2 for any values of m nd n, what is the value of ( 2 cp 4)? express your answer as a common fraction.
That cp thingy is just a symbol they created to define a specific operation. I'll use $\spadesuit$ instead.

If $(m\; \spadesuit \;n)=\frac{1}{m}+\frac{1}{n}+\frac{1}{m^2}+\frac{1 }{n^2}$, then

$(2\; \spadesuit \;4)=\frac{1}{2}+\frac{1}{4}+\frac{1}{2^2}+\frac{1 }{4^2}$

$(2\; \spadesuit \;4)=\frac{1}{2}+\frac{1}{4}+\frac{1}{4}+\frac{1}{ 16}=\boxed{\frac{17}{16}}$