Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Two friends visited a taffy shop. Colin bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $25. Next, Keenan bought 1 kilogram of banana taffy for $5. How much does the candy cost? A kilogram of strawberry taffy costs $_____, and a kilogram of banana taffy costs $_____.

Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.  Two friends visited a taffy shop. Colin bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $25. Next, Keenan bought 1 kilogram of banana taffy for $5. How much does the candy cost?  A kilogram of strawberry taffy costs $_____, and a kilogram of banana taffy costs $_____.

Bytelearn · Accepted Answer

Define Variables:  Let's call the price of strawberry taffy per kilogram s and the price of banana taffy per kilogram b. Colin's purchase gives us the equation 4s + b = 25. Keenan's purchase gives us the equation b = 5. Write Augmented Matrix:  We can write the system of equations as an augmented matrix. The first row represents Colin's purchase, and the second row represents Keenan's purchase. So we have: $$ \begin{bmatrix} 4 & 1 & | & 25 \ 0 & 1 & | & 5 \end{bmatrix} $$Eliminate Variable:  Since the second row already has a leading 1 in the second column, we can use it to eliminate the b variable from the first row. We'll multiply the second row by -1 and add it to the first row. Correct Mistake:  After the row operation, the new matrix is: $$ \begin{bmatrix} 4 & 0 & | & 20 \ 0 & 1 & | & 5 \end{bmatrix} $$ Oops, I made a mistake. I should have multiplied the second row by -1 and then multiplied it by 4 before adding it to the first row to eliminate b.

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