Question

The Boy Scouts self popcorn Ethan sold 9 small

And 2 large he made $36.05. jack sold 5 small
And 7 large and made $48.find the cost of small and large bag popcorn

Answer 1

The price of small popcorn is $ 2.95 and

The price of large popcorn is $ 4.75

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 =
`(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 =
`(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

Answer 2

The cost of 1 small bag of popcorn = $2.95

The cost of 1 large bag of popcorn = $4.75

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