Question

Julie and her friend went to the movies and bought one jumbo popcorn and two chocholate chip cookies for 5$. Marvin and his friend went to the same movies and bought 3 jumbo popcorns and 5 chocolate chip cookies $14.50. Set up and solve a system of equations to determine the cost of one jumbo and one chocolate chip cookie.

Answer 1

Let j = cost of one jumbo popcorn, and c = cost of one chocolate chip cookie.

Then, based upon the given info, 1j + 2c = $5.

Also, 3j + 5c = $14.50

Let's solve this system of equations using addition/subtraction:

Mult. the first equation by -3, to obtain   -3j - 6c = -$15

Now add this result to the 2nd equation:   

-3j - 6c = -$15
3j + 5c = $14.50
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     -c = -$0.50, or c = $0.50.       Since   3j + 5c = $14.50, subst. $0.50 for c 
lets us find j:

3j + 5($0.50) = $14.50, so 3j = $12.00.  Thus, j = $4.00.


Jumbo popcorn is $4/bag, and choc. chip cookies $0.50 each.