Question 214816
For Halloween, Mr. Olowitz bought 8 bags of candy bars and 4 bags of lollipops for a total cost of $51.56. Later that day he realized he didn’t have enough candy and went back to the same store and bought 3 more bags of candy bars and 3 more bags of lollipops at the same prices for a total cost of $23.82. While in the store on his second trip, Mr. Olowitz ran into his neighbor, Mrs. Pinion. If Mrs. Pinion bought 3 bags of candy bars and 11 bags of lollipops at the same prices, what was her total cost?


Step 1.  Let x be the cost for one bag of candy bars.


Step 2.  Let y be the cost for one bag of lollipops.


Step 3.  Let 8x+4y=51.56  be the cost of 8 bags of candy bars and 4 bags of lollipops for a total cost of $51.56.


Step 4.  Let 3x+3y=23.82  be the cost of 3 more bags of candy bars and 3 more bags of lollipops at the same prices for a total cost of $23.82.


Step 5.  The following will solve the system of equations in Steps 3 and 4 using substitution.


*[invoke linear_substitution "x", "y", 8,4,51.56, 3,3,23.82 ]


Step 6.  Given that x=4.95 and y=2.99  , and Mrs. Pinion bought 3 bags of candy bars and 11 bags of lollipops at the same prices. Then.


{{{3x+11y= 3*4.95+11*2.99=47.74}}}


Step 7.  ANSWER:  The total cost for Mrs. Pinion is $47.74.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J