A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
7/16
7/15
10/21
17/35
1/2
Fraction of Revenue
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A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
3/5 small, 2/5 large
large price : small 7:6
revenue large = 2/5 * 7 = 14/5
total revenue = 14/5 + (6*3/5) = 32/5
fraction of total = 14/5 / 32/5 = 14/32 = 7/16
u can also plugin numbers
say total cups = 25
small = 3/5 * 25 = 15, large = 10
say price for small = 12, large = 14
revenue large = 10*14 = 140
total revenue = 140 + 180 = 320
fraction of total = 140/320 = 7/16
3/5 small, 2/5 large
large price : small 7:6
revenue large = 2/5 * 7 = 14/5
total revenue = 14/5 + (6*3/5) = 32/5
fraction of total = 14/5 / 32/5 = 14/32 = 7/16
u can also plugin numbers
say total cups = 25
small = 3/5 * 25 = 15, large = 10
say price for small = 12, large = 14
revenue large = 10*14 = 140
total revenue = 140 + 180 = 320
fraction of total = 140/320 = 7/16
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We can also solve this question by plugging in some numbers that satisfy the given information.GmatKiss wrote:A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
7/16
7/15
10/21
17/35
1/2
To begin, we're told that 3/5 of the cups sold were small and the rest were large, so let's say that a total of 5 cups were sold.
This means that 3 small cups were sold, and 2 large cups were sold.
Next, if large cups were sold for 7/6 as much as the small cups, we can say that small cups cost $6 each, and large cups cost $7 each.
Revenue from small cups = 3 x $6 = $18
Revenue from large cups = 2 x $7 = $14
Total revenue = $18 + $14 = $32
So, fraction of revenue from sale of large cups = $14/$32 = 7/16
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Brent
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We can let the total number of cups = n. Since 3/5 of the cups that were sold were small, (3/5)n = the number of small cups sold and (2/5)n = the number of large cups sold.GmatKiss wrote:A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
7/16
7/15
10/21
17/35
1/2
Also, if we let the price of each small cup = p, then the price for each large cup = (7/6)p.
The revenue from the sale of large cups is (7/6)p * (2/5)n = (7/15)np and the revenue from the sale of small cups is p * (3/5)n = (3/5)np. Therefore, the total revenue from the sale of all the cups is (7/15)np + (3/5)np = (7/15)np + (9/15)np = (16/15)np.
We can now determine what fraction of Tuesday's total revenue was from the sale of large cups.
[(7/15)np]/[(16/15)np] = (7/15)/(16/15) = 7/16
Alternate Solution:
Let's denote the total number of cups sold by 5n in which n is an integer. Since 3/5 of the number of cups sold were small, the number of small cups that were sold is (5n)(3/5) = 3n. Similarly, since 1 - 3/5 = 2/5 of the number of cups sold were large, the number of large cups that were sold is (5n)(2/5) = 2n.
Also, let's denote the price of each small cup as6p. Then, the price of a large cup was (6p)(7/6) = 7p.
Now, the revenue earned from small cups was (3n)(6p) = 18np and the revenue earned from large cups was (2n)(7p) = 14np. In total, a revenue of 18np + 14np = 32np was earned. The large cups constituted 14np/32np = 7/16 of this revenue.
Answer: A
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