At a certain coffee shop, a mocha sells for $3.00 and a cappuccino sells for $2.25. In total, the shop sold $180 worth

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

At a certain coffee shop, a mocha sells for $3.00 and a cappuccino sells for $2.25. In total, the shop sold $180 worth

by BTGmoderatorDC » Wed May 20, 2020 5:56 pm

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At a certain coffee shop, a mocha sells for $3.00 and a cappuccino sells for $2.25. In total, the shop sold $180 worth of mochas and cappuccinos over the course of a day. How many mochas did the shop sell?

(1) The shop sold 10 more cappuccinos than it did mochas.
(2) The combined price of all of the cappuccinos sold was equal to the combined price of all of the mochas sold.

OA D

Source: Manhattan Prep

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Source: Beat The GMAT — Data Sufficiency | Wed May 20, 2020 5:56 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: At a certain coffee shop, a mocha sells for $3.00 and a cappuccino sells for $2.25. In total, the shop sold $180 wor

by deloitte247 » Sun May 24, 2020 12:28 am

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Let mocha = m and cappucino = c
1m = $3.00 and 1c = $2.25
Let number of m sold = x
Let number of c sold = y
xm + cy = $180

Target question => How many mochas did the shop sell? i.e find x
$$\frac{xm}{m}=\frac{180-cy}{m}\ \ \ where\ m\ =\ 3\ and\ y\ =\ 2.25$$
$$x=\frac{180-2.25y}{3}$$

Statement 1 => The shop sold 10 more cappuccinos than it did mochas
i.e y = 10 + x
$$From\ question\ stem=>x=\frac{180-2.25y}{3}\ \ \ where\ y\ =\ 10+x$$
$$x=\frac{180-2.25\left(10+x\right)}{3}\ \ \ $$
$$3x=180-22.5-2.25x$$
$$collect\ like\ terms$$
$$\frac{5.25x}{5.25}=\frac{157.5}{5.2x}\ \ \ \ \ \ x\approx30$$
Statement 1 is SUFFICIENT

Statement 2 => The combined price of all of the cappuccinos sold was equal to the combined price of all of the mochas sold
i.e 2.25y = 3x
$$From\ question\ stem\ =>\ x=\frac{180-2.25y}{3}\ \ where\ 2.25y=3x$$
$$3x=180-3x$$
$$\frac{6x}{6}=\frac{180}{6}\ and\ \ x=30$$
Statement 2 is SUFFICIENT

Since each statement alone is SUFFICIENT
Answer = D