Q. 419

Question

The church youth group is

selling snacks to raise money to

attend their convention. Amy sold

2 pounds of candy, 3 boxes of

cookies and 1 can of popcorn for

a total sales of \(65. Brian sold 4

pounds of candy, 6 boxes of

cookies and 3 cans of popcorn for

a total sales of \)140. Paulina sold

8 pounds of candy, 8 boxes of

cookies and 5 can of popcorn for a

total sales of $250. What is the cost

of each item?

Step-by-Step Solution

Verified

Answer

The cost of candies is $20 $$ , cost of boxes of cookies is $5 $$ and that of popcorn is $10 $$ .

1Step 1. Given information.

Amy sold:

2 pound of candies, 3 boxes of cookies and 1 can of popcorn.

Brian sold:

4 pounds of candy, 6 boxes of

cookies and 3 cans of popcorn.

Paulina sold :

8 pounds of candy, 8 boxes of

cookies and 5 can of popcorn.

Their total worth are:

$65 $ 140 $ 250 $$

2Step 2. Write the concept.

Let the price of candies be $x $$ ,price of cookies be $y $$ and price of popcorn be $z $$ .

Therefore equation framed will be:

$2 x + 3 y + z = 65 . . . . . . . . (1) 4 x + 6 y + 3 z = 140 . . . . . (2) 8 x + 8 y + 5 z = 250 . . . . . . (3)$

3Step 3. Calculation.

$2 x + 3 y + z = 65 . . . . . . . . (1) 4 x + 6 y + 3 z = 140 . . . . . (2) 8 x + 8 y + 5 z = 250 . . . . . . (3) M u l t i p l y i n g 2 w i t h e q u a t i o n (1) a n d s u b t r a c t i n g w i t h e q u a t i o n (2) w e g e t : S o l v e f o r z : (4 x + 6 y + 3 z) - (4 x_6 y - 2 z) = 140 - 130 z = 10 N o w s u b s t i t u t i n g v a l u e o f z i n e q (1) a n d (2) 2 x + 3 y = 55 . . . . . . . . . . (3) 4 x + 6 y = 110 . . . . . . . . . (4) S o l v e f o r y : c o n s i d e r i n g e q (3) a n d e q (1) w e g e t 2 x + 3 y = 55 8 x + 8 y = 200 M u l t i p l y i n g 2 w i t h e q (3) a n d s u b t r a c t i n g w i t h e q (4) w e g e t : (8 x + 12 y) - (8 x + 8 y) = 220 - 200 4 y = 20 y = 5 S o l v e f o r x : p u t t h e v a l u e s o f x, y a n d z i n e q (1) 2 x + 3 (5) + 10 = 65 x = 20$