Problem Solving

BTGmoderatorDC wrote: ↑

Mon Mar 15, 2021 12:17 am

In a certain drink, the ratio of vodka to orange juice is 2 : 3, and the ratio of orange juice to tonic water is 2 : 1. If 3 ounces of tonic water are added to the drink, and enough orange juice is also added to keep the proper proportions, how many more ounces of vodka must be added in order to maintain the correct overall mixture?

a. 1
b. 2
c. 4
d. 6
e. 9


OA C

Solution:

We have v : o as 2 : 3 and o : t as 2 : 1. We must reconfigure these two ratios to make them compatible. The way to do this is to “match” the numbers for orange juice with the common multiple of 6. Thus, the first ratio will now be v : o is 4 : 6, and the second ratio will now be o : t is 6 : 3. The 3-way ratio can now be expressed as v : o : t is 4 : 6 : 3.


Vodka : OJ: Tonic Water = 4x : 6x : 3x

If we let x = 1, then we currently have 4 ounces, 6 ounces and 3 ounces of vodka, OJ, and tonic water, respectively, in the drink.

If 3 ounces of tonic water is added, then we would have 6 ounces of tonic water, and we would need to have 12 ounces of OJ and 8 ounces of vodka. So we need 4 more ounces of vodka.

Answer: C