# define variables, write equations, solve

#### cathyv

Food stand sells popcorn for $2.50 and pretzels for$2.00. Sells $336 worth of popcorn and pretzels. They sell twice as many bags of popcorn as pretzels. How many of each do they sell? thank you! #### tkhunny ##### Moderator Staff member You appear to have excellent instructions. Why not follow them? Let's see what you get for your variable definitions. #### cathyv ##### New member p=pretzels 2p=popcorn 2p+5p=336 7p=336 p=48 2p=96 did I figure it out? #### tkhunny ##### Moderator Staff member Let's see...did you check your answers against the problem statement? Does p = 48 work? Clean and precise will help you gain confidence and consistency. Here's an example. I would do it this way. Definitions: Z = Bags of Pretzels Sold C = Bags of Popcorn Sold What does it want? "How many of each do they sell?" Okay, so we'll need Z and C before we think we are done. Equation Translation: "They sell twice as many bags of popcorn as pretzels." 1) C = 2Z "popcorn for$2.50 and pretzels for $2.00. Sells$336 worth of popcorn and pretzels.

2) $2.50 * C +$2.00 * Z = $336 Solution: It appears that eauation 1 is already solved for "C", so simply substitute for "C" in equation 2. 3)$2.50 * (2Z) + $2.00 * Z =$336

Simplify and solve for Z

4) $5.00 * Z +$2.00 * Z = $336 (Substitution) 5)$7.00 * Z = $336 (Distributive Property) 6) Z =$336 / $7.00 = 48 Substitute this value of Z into equation 1 7) C = 2(48) = 96 Checking: From Equation 1: 96 = 2*48 ==> 96 = 96 -- Check From Equation 2:$2.50 * (96) + $2.00 * (48) =$336 ==> $240.00 +$96 = $336 ==>$336 = \$336 -- Check