VJesus12 wrote:A soda machine sells both bottles and cans, and no other items. Bottles cost $1.50 each, while cans cost $0.75 each. If on one day, the soda machine sold 250 total beverages and yielded $315, how many more bottles than cans were sold?
A) 60
B) 80
C) 90
D) 115
E) 170
Price per bottle = 150 cents.
Price per can = 75 cents.
Average price for the MIXTURE of bottles and cans = (total revenue)/(total number of beverages) = (315 dollars)/(250 beverages) = 63/50 dollars = 126/100 dollars = 126 cents.
To determine the ratio of bottles to cans, we can use ALLIGATION.
Step 1: Plot the 3 prices on a number line, with the prices for bottles and canes on the ends and the price for the mixture in the middle.
B 150---------------------126----------------------75 C
Step 2: Calculate the distances between the averages.
B 150---------
51---------126---------
24---------75 C
Step 3: Determine the ratio in the mixture.
The ratio of bottles to cans is equal to the RECIPROCAL of the distances in red.
B:C = 24:51 = 8:17 =
80:170.
The ratio in blue implies that B=80 and C=170, for a total of 250 beverages.
Thus:
C-B = 170-80 = 90.
The correct answer is
C.
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