Mathematics: Amerchant 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?

Equation of the line:y = 0.25x – 1...

Amerchant has coffee worth $20 a pound that she - id20867960, alshaibanihassan10

isaaccott013

12.03.2022

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 pounds.

The merchant wants to mix that 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 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 as shown below:

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

Divide both sides by in above equation as follows:

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

Therefore, the value of is 420 .

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

Learn more:

1. Learn more about equations

2. Learn about solving equation

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.

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