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?

The amount of coffee is .

Further explanation:

Given information:

A merchant has a pound of coffee of worth .  

That merchant wants to mix of coffee that worth a pound with the coffee that’s worth is .

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

Calculation:

Let us consider the amount of coffee be pounds.

The merchant wants to mix that pound of coffee with of coffee.

Therefore, the total mixture would be of pounds.

Now, the total worth of the mixture of coffee and coffee is calculated as  follows:

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

Therefore, the merchant’s earning would be dollars.

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

Therefore, the amount of coffee can be calculated as  follows:

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

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

Divide both sides by in above equation as  follows:

Therefore, the value of is .

Thus, the amount of coffee is .

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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i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn