Problem Solving

BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:09 am

Last year $48,000 of a certain store's profit was shared by its 2 owners and their 10 employees. Each of the 2 owners received 3 times as much as each of their 10 employees. How much did each owner receive from the $48,000 ?

A. $12,000

B. $9,000

C. $6,000

D. $4,000

E. $3,000

Answer: B
Source: Official guide

Each owner received 3 times as much as each employee
Let E = the amount (in dollars) that ONE employee received
So, 3E = the amount (in dollars) that ONE owner received

Last year $48,000 of a certain store's profit was shared by its 2 owners and their 10 employees.
In other words: 3E + 3E + E + E + E + E + E + E + E + E + E + E = 48,000
Simplify: 16E = 48,000
So, E = 48,000/16
= 3,000

So, each EMPLOYEE received $3000, which means each OWNER received $9000
Answer: B

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:09 am

Last year $48,000 of a certain store's profit was shared by its 2 owners and their 10 employees. Each of the 2 owners received 3 times as much as each of their 10 employees. How much did each owner receive from the $48,000 ?

A. $12,000

B. $9,000

C. $6,000

D. $4,000

E. $3,000

Answer: B
Source: Official guide

Although I believe it's best to use one variable to solve this question, we can also use two variables
Let's see how that solution would look.

Let x = the amount (in dollars) that ONE employee received
Let y = the amount (in dollars) that ONE owner received

Each owner received 3 times as much as each employee
So, we can write: y = 3x

Last year $48,000 of a certain store's profit was shared by its 2 owners and their 10 employees.
So, the total amount two owners received = y + y = 2y
The total amount 10 employees received = 10x
So, we can write: 10x + 2y = 48,000

At this point, we have the following system of linear equations:
y = 3x
10x + 2y = 48,000

When we solve this system (I'll leave it to you to do this), we get x = 3000 and y = 9000
So, each each OWNER received $9000

Answer: B

Cheers,
Brent