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

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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) About Me  (Show Source):
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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.

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++8%5Cx+%2B+4%5Cy+=+51.56%2C%0D%0A++++3%5Cx+%2B+3%5Cy+=+23.82+%29%0D%0A++We'll use substitution. After moving 4*y to the right, we get:
8%2Ax+=+51.56+-+4%2Ay, or x+=+51.56%2F8+-+4%2Ay%2F8. Substitute that
into another equation:
3%2A%2851.56%2F8+-+4%2Ay%2F8%29+%2B+3%5Cy+=+23.82 and simplify: So, we know that y=2.99. Since x+=+51.56%2F8+-+4%2Ay%2F8, x=4.95.

Answer: system%28+x=4.95%2C+y=2.99+%29.



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%2B11y=+3%2A4.95%2B11%2A2.99=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