Archie can buy 5 buckets of popcorn and 2 drinks for $16.25. terry can buy 3 buckets of popcorn and 1 drinks for $9.50. assume that all buckets of popcorn are the same price and all drinks are the same price.

The cost of one bucket of popcorn is $2.75

The cost of one drink is $1.25

Step-by-step explanation:

Let

x > the cost of one bucket of popcorn

y > the cost of one drink

we know that

5x+2y=16.25 > equation A

3x+y=9.50

y=9.50-3x > equation B

Solve the system of equations by substitution

Substitute equation B in equation A and solve for x

5x+2(9.50-3x)=16.25

5x+19-6x=16.25

6x-5x=19-16.25

x=$2.75

Find the value of y

y=9.50-3x

y=9.50-3(2.75)=$1.25

therefore

The cost of one bucket of popcorn is $2.75

The cost of one drink is $1.25

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

a

step-by-step explanation: