Question

The Boy Scouts self popcorn Ethan sold 9 small

Answer 1

Answer:

The cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag of popcorn   = $4.75

Step-by-step explanation:

Here, let us assume the cost of 1 small bag of popcorn = $ m

And,  the cost of 1 large bag of popcorn = $ n

So, the cost of 9 small bag = 9 x ( cost of 1 small bag)  = 9 x (m) = 9 m

and  the cost of 2 large bag = 2 x ( cost of 1 large bag)  = 2 x (n) = 2 n

Also, cost of 9 small + 2 large bag of popcorn sold by  Ethan for   $ 36.05 .

⇒ Total cost of 9 small + 2 large bag of popcorn =  9 m + 2 n

⇒ 9  m +  2 n =  $ 36.05  ..........  (1)

Also, the cost of 5 small bag = 5 x ( cost of 1 small bag)  = 5 m

and  the cost of 7 large bag = 7 x ( cost of 1 large bag)  = 7 n

Also, cost of 5 small + 7 large bag of popcorn sold by  Jack for   $ 48 .

⇒ Total cost of 5 small + 7 large bag of popcorn =  5 m + 7 n

⇒ 5 m +  7 n =  $ 48 ..........  (2)

Now, solving (1) and (2) for the values of m and n , we get

9  m +  2 n =   36.05

5 m +  7 n =  48

Multiply (1) with (-7) and (2) by 2 , add both equation we get:

-63 m - 14 n  + 10 m + 14 n =  -252.35 + 96

or, - 53 m = -156.35

or, m =   2.95

Now, put the value of m in (1), we get:  5 ( 2.95) + 7 n =  48

or, n =  33.25 /7 = 4.75

Hence the cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag  = $4.75

Answer 2

Answer:

The price of small popcorn is $ 2.95  and  

The price of large popcorn is $ 4.75

Step-by-step explanation:

Given as :

The price for 9 small and 2 large popcorn = $ 36.05

The price of 5 small and 7 large popcorn = $ 48

let the small popcorn = S

And The larger popcorn = L

Now, According to question

9 S + 2 L = $ 36.05

5 S  +7 L = $ 48

Solving the equation

Or, 7×(9 S + 2 L) = 7×36.05

Or , 63 S + 14 L = 252.35       ....A

And

2×(5 S + 7 L) = 2×48

Or, 10 S + 14 L = 96               .......B

Solving Eq A and B

Or, ( 63 S + 14 L ) - ( 10 S + 14 L ) = 252.35 - 96

Or, ( 63 S- 10 S ) + ( 14 L - 14 L ) = 156.35

Or, 53 S + 0 = 156.35

∴  S = $\frac{156.35}{53}$

I.e S = 2.95

So, the price of small popcorn = $ 2.95

Again put the value of S in Eq B

Or, ( 10 × 2.95 ) + 14 L = 96

Or, 29.5 + 14 L = 96

Or, 14 L = 96 - 29.5

Or, 14 L = 66.5

∴ L = $\frac{66.5}{14}$

I.e L = 4.75

So The price of large popcorn = $ 4.75

Hence The price of small popcorn is $ 2.95  and  The price of large popcorn is $ 4.75  Answer