Question

A merchant has coffee worth $20 a pound that she wishes to mix with 70 pounds of coffee worth $90 a pound to get a mixture that she will sell for $30 a pound. How many pounds (lb) of the $20 coffee should be used?

Answer 1

The amount of $\ \ 20$ coffee is $\boxed{\bf 420\text{\bf pounds}}$.

Further explanation:

Given information:

A merchant has a pound of coffee of worth $\ \ 20$.  

That merchant wants to mix $70\text{ pounds}$ of coffee that worth $\ \ 90$ a pound with the coffee that’s worth is $\ \ 20$.

After that the merchant wants to sell that mixture for $\ \ 30$ a pound.

Calculation:

Let us consider the amount of $\ \ 20$ coffee be $x$ pounds.

The merchant wants to mix that $x$ pound of $\ \ 20$ coffee with $70\text{ pounds}$ of $\ \ 90$ coffee.

Therefore, the total mixture would be of $(x+70)$ pounds.

Now, the total worth of the mixture of $\ \ 20$ coffee and $\ \ 90$ coffee is calculated as  follows:

$\boxed{(20\cdot x)+(90\cdot 70)=20x+6300}$

The merchant wants to sell the total mixture for $\ \ 30$ a pound.

Therefore, the merchant’s earning would be $30(x+70)$ dollars.

The worth of the mixture would be equal to the total earnings.

Therefore, the amount $x$ of $\ \ 20$ coffee can be calculated as  follows:

$\boxed{30(x+70)=20x+6300}$

 

Use distributive property to expand the Left-Hand Side of above equation as follows:

$\begin{aligned}(30\cdot x)+(30\cdot 70)&=20x+6300\\30x+2100&=20x+6300\end{aligned}$

 

Simplify the above equation to find the value of $x$ as shown below:

$\begin{aligned}30x-20x&=6300-2100\\10x&=4200\end{aligned}$  

Divide both sides by $10$ in above equation as  follows:

$\begin{aligned}\dfrac{10x}{10}&=\dfrac{4200}{10}\\x&=420\end{aligned}$

Therefore, the value of $x$ is $420$.

Thus, the amount of $\ \ 20$ coffee is $\boxed{\bf 420\text{\bf pounds}}$.

Learn more:

1. Learn more about equations brainly.com/question/1473992

2. Learn about solving equation brainly.com/question/5723059

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations

Keywords: Merchant, coffee, $20, $90, $30, pounds, 70 pounds, 420 pounds, x, mixture, sell, mix, equation, linear, amount, distributive property.

Answer 2

Let us start with assuming the amount of coffee worth $20 a pound to be "x" pounds.

Now she wants to mix "x" pounds of $20 coffee with 70 pounds of $90 coffee.

So the mixture would be (x + 70) pounds.

And the value of mixture would be = 20·x + (90)·(70) = (20x + 6300) dollars.

She want to sell this mixture at rate of $30 a pound. Her earning would be = 30·(x + 70) = (30x + 2100) dollars.

We know that the value of mixture would be equal to her earnings.

30x + 2100 = 20x + 6300

30x - 20x = 6300 - 2100

10x = 4200

x = 420

So, 420 pounds of $20 coffee would be used.