Cookies are on sale! Today each cookie costs $0.75 less than the normal price. Right now if you...

Question:

Cookies are on sale! Today each cookie costs $0.75 less than the normal price. Right now if you buy 7 of them it will only cost you $2.80! Write an equation to determine the normal price of each cookie.

Algebraic Expression:

Algebraic expressions are mathematical relationship of variables, numbers or integers, and algebraic operations. Algebraic expression is used to describe how variables is related to one another and is used extensively to solve for unknown values given known values.

Answer and Explanation:

Let {eq}P {/eq} be the normal price of the cookie, that is, the price of the cookie when not in sale. Now, today the cookie costs {eq}0.75 {/eq} less than the normal price, then we write the cookie price of today as

$$P-0.75 $$

If we buy {eq}7 {/eq} cookies today, it will costs us {eq}2.80 {/eq}. Writing this into equation using the cookie price today

$$2.80=7\times \left(P-0.75\right) \\ $$

Right now, we have one unknown value {eq}P {/eq}, then solving for it

$$\begin{align} 2.80&=7\times \left(P-0.75\right) \\ \frac{2.80}{7}&=\left(P-0.75\right) \\ P-0.75&=\frac{2.80}{7} \\ P&=\frac{2.80}{7}+0.75 \\ P &= 1.15 \end{align} $$

Hence, the normal price of the cookie is {eq}\boxed{1.15 \hspace{1mm} \$} {/eq}.


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