Problem Solving

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:45 pm

Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275
B. $325
C. $425
D. $575
E. $625

Answer: B
Source: Magoosh

This question lends itself nicely to testing the answer choices

We'll start with answer choice C ($425), the middle value.
If Alice paid $425, how much did Bruce pay?
Given: twice of what Alice paid was $75 more than what Bruce paid
Two times $425 = $850, so Bruce paid $775 (since $850 - $75 = $775
COMBINED PAYMENTS = $425 + $775 = $1200
No good - we need the combined payments to be $900
ELIMINATE C
We can also ELIMINATE D and E, because those values will yield an even greater values of the combined payments.

Now let's try B ($325)
Given: twice of what Alice paid was $75 more than what Bruce paid
Two times $325= $650, so Bruce paid $575 (since $650 - $75 = $575
COMBINED PAYMENTS = $325 + $575 = $900
Perfect!!!

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:45 pm

Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275
B. $325
C. $425
D. $575
E. $625

Answer: B
Source: Magoosh

We can also solve the question algebraically, using 1 variable or 2 variables.
Here's a solution with 1 variable:

Given: Twice of what Alice paid was $75 more than what Bruce paid
Let x = the amount Alice paid
So, 2x - 75 = the amount Bruce paid

Given: The sum of their purchases was $900
So, (the amount Alice paid) + (the amount Bruce paid) = 900
We get: x + (2x - 75) = 900
Simplify: 3x - 75 = 900
Solve: x = 325

Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:45 pm

Alice and Bruce each bought a refrigerator, and the sum of their purchases was $900. If twice of what Alice paid was $75 more than what Bruce paid, what did Alice pay for her refrigerator?

A. $275
B. $325
C. $425
D. $575
E. $625

Answer: B

Solution:

We can let a = the amount Alice paid and b = the amount Bruce paid. Thus we have:

a + b = 900

and

2a = b + 75

Thus, b = 2a - 75. Substituting this into the first equation, we have:

a + 2a - 75 = 900

3a = 975

a = 325

Answer: B