Next year, if Company Q produces x units of a certain product and sell

Question

Next year, if Company Q produces x units of a certain product and sells y units of this product, its total profit, in dollars, from this product will be 10y— 4x. If x and y are related by the equation y = rx and if Company Q's average (arithmetic mean) profit per item produced next year must be at least $4.50, what is the least possible value of r?

A. 0.65
B. 0.70
C. 0.75
D. 0.80
E. 0.85

A. 0.65
B. 0.70
C. 0.75
D. 0.80
E. 0.85

gmatophobia · Accepted Answer

Given

Profit = 10y— 4x

Profit per product produced (or average profit per product) =  \frac{10y— 4x }{ x}

If x and y are related by the equation y = rx

Profit per product produced =  \frac{10rx— 4x }{ x}

if Company Q's average (arithmetic mean) profit per item produced next year must be at least $4.50

\frac{10rx— 4x }{ x} \geq 4.50

10rx— 4x \geq 4.50x

As x denotes the number of products, x is a positive integer. We can divide both sides of the equation by x

10r— 4 \geq 4.50

10r \geq 8.50

r \geq 0.850

The least possible value of r = 0.85

Option E

GMATCoachBen · Answer

The key is to build fluency in translating these word-for-word into equations.

I break down the process here (2:53): 
 
 https://www.youtube.com/watch?v=T2SX7V3MCEQ

JeffTargetTestPrep · Answer

x = # produced

y = # sold

10y – 4x = total profit

y = rx

The following inequality must be true:

(10y – 4x)/x ≥ 4.5

(10rx – 4x)/x ≥ 4.5

10r – 4 ≥ 4.5

10r ≥ 8.5

r ≥ 0.85

Therefore, the least possible value of r is 0.85.

Answer: E

Jake7Wimmer · Answer

Can anyone show how to do this using the answering choices or a different method than doing it algebraically.

Bunuel · Answer

I'd say that the algebraic approach demonstrated above is the most effective method for tackling this question. Once you grasp it, the question simplifies significantly. I recommend revisiting the solutions provided and asking if anything still seems unclear.

KarishmaB · Answer

Profit = 10y— 4x 
and  y = rx

Reduce the number of variables as much as you can. Plug in y in Profit so that we don't have to worry about it.

Profit = 10*rx— 4x= x(10r -4)

We are given that average profit per item = $4.5. How do we find "average profit per item"? It is Profit/Number of items = Profit/x

From above,  \frac{Profit}{x} = 10r-4 = 4.5 
 r = 0.85

Answer (E)

hemanthPA · Answer

Manufacture: X units
Sell: y units
Profit = Revenue – cost = 10y – 4x
Y = rx
Avg profit/item = 4.5

R = ?

Profit per product produced = 10y – 4x/x

4.5 = 10(rx) – 4x/x
4.5 = 10r-4
10r = 8.5
R = 0.85

kashisshhhhh · Answer

Hi Scott,

I divided the total profit by y instead of x. A little confused there, can you help please?

Thanks

Bunuel · Answer

You should divide by x because the question asks for average profit  per item produced , not per item sold.

Next year, if Company Q produces x units of a certain product and sells y units of this product, its total profit, in dollars, from this product will be 10y— 4x. If x and y are related by the equation y = rx and if Company Q's average (arithmetic mean) profit per item produced next year must be at least $4.50, what is the least possible value of r?

A. 0.65
B. 0.70
C. 0.75
D. 0.80
E. 0.85

Rudraksh464 · Answer

i dont understand, shouldnt total no of items be y?
x is the total no of units produced, y is the total no. of units sold. 
profit per unit should equal- Total Profit / No of units sold
why is it Total Profit/ No of units produced?

Bunuel · Answer

Have you checked  this post ?

Next year, if Company Q produces x units of a certain product and sell

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Next year, if Company Q produces x units of a certain product and sell

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