SOLUTION: 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
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?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website! 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.
Solve: We'll use substitution. After moving 4*y to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that y=2.99. Since , x=4.95.
Answer: .
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.
Step 7. ANSWER: The total cost for Mrs. Pinion is $47.74.
I hope the above steps were helpful.
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