manalq8 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?

A. 7/16

B. 7/15

C. 10/21

D. 17/35

E. 1/2

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.

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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