Patty is ordering vests for her scout troop to wear in the Veterans Day parade. She ordered $12$ vests from the Festive Features clothing shop. Since this was a bulk order, Festive Features reduced the price of each vest by $\$ 6$ . The total came to $\$ 132$ . $\newline$ Which equation can you use to find the amount, $v$ , Festive Features normally charges for a vest? $\newline$ $12 v-6=132$ $\newline$ $12(v-6)=132$ $\newline$ $6(v-12)=132$ $\newline$ $6 v-12=132$ $\newline$ How much does Festive Features normally charge for a vest? $\newline$ $\$ \square$

Full solution

Q. Patty is ordering vests for her scout troop to wear in the Veterans Day parade. She ordered

12

vests from the Festive Features clothing shop. Since this was a bulk order, Festive Features reduced the price of each vest by

\$ 6

. The total came to

\$ 132

\newline

Which equation can you use to find the amount,

v

, Festive Features normally charges for a vest?

\newline

12 v-6=132

\newline

12(v-6)=132

\newline

6(v-12)=132

\newline

6 v-12=132

\newline

How much does Festive Features normally charge for a vest?

\newline

\$ \square

Understand the problem: Understand the problem. $\newline$ Patty ordered $12$ vests and got a discount of $\$6$ per vest. The total cost was $\$132$ . We need to find the original price of each vest before the discount.
Set up the equation: Set up the equation. $\newline$ The total cost for the vests after the discount is given by the number of vests times the discounted price per vest. The discounted price per vest is the original price $v$ minus the discount ( $\$6$ ). So the equation is $12(v - 6) = 132$ .
Choose the correct equation: Choose the correct equation from the options. $\newline$ The correct equation that represents the situation is $12(v - 6) = 132$ , because it shows the total cost after a discount of $\$6$ per vest for $12$ vests.
Solve the equation for $v$ : Solve the equation for $v$ . $12(v - 6) = 132$ Divide both sides by $12$ to isolate the term $(v - 6)$ : $v - 6 = \frac{132}{12}$ $v - 6 = 11$ Now, add $6$ to both sides to solve for $v$ : $v = 11 + 6$ $v = 17$
Verify the solution: Verify the solution. $\newline$ To verify, plug the value of $v$ back into the equation: $\newline$ $12(v - 6) = 132$ $\newline$ $12(17 - 6) = 132$ $\newline$ $12(11) = 132$ $\newline$ $132 = 132$ $\newline$ The solution is correct.