Respuesta :
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.
The amount of [tex]\$\ 20[/tex] coffee is [tex]\boxed{\bf 420\text{\bf pounds}}[/tex].
Further explanation:
Given information:
A merchant has a pound of coffee of worth [tex]\$\ 20[/tex].
That merchant wants to mix [tex]70\text{ pounds}[/tex] of coffee that worth [tex]\$\ 90[/tex] a pound with the coffee that’s worth is [tex]\$\ 20[/tex].
After that the merchant wants to sell that mixture for [tex]\$\ 30[/tex] a pound.
Calculation:
Let us consider the amount of [tex]\$\ 20[/tex] coffee be [tex]x[/tex] pounds.
The merchant wants to mix that [tex]x[/tex] pound of [tex]\$\ 20[/tex] coffee with [tex]70\text{ pounds}[/tex] of [tex]\$\ 90[/tex] coffee.
Therefore, the total mixture would be of [tex](x+70)[/tex] pounds.
Now, the total worth of the mixture of [tex]\$\ 20[/tex] coffee and [tex]\$\ 90[/tex] coffee is calculated as follows:
[tex]\boxed{(20\cdot x)+(90\cdot 70)=20x+6300}[/tex]
The merchant wants to sell the total mixture for [tex]\$\ 30[/tex] a pound.
Therefore, the merchant’s earning would be [tex]30(x+70)[/tex] dollars.
The worth of the mixture would be equal to the total earnings.
Therefore, the amount [tex]x[/tex] of [tex]\$\ 20[/tex] coffee can be calculated as follows:
[tex]\boxed{30(x+70)=20x+6300}[/tex]
Use distributive property to expand the Left-Hand Side of above equation as follows:
[tex]\begin{aligned}(30\cdot x)+(30\cdot 70)&=20x+6300\\30x+2100&=20x+6300\end{aligned}[/tex]
Simplify the above equation to find the value of [tex]x[/tex] as shown below:
[tex]\begin{aligned}30x-20x&=6300-2100\\10x&=4200\end{aligned}[/tex]
Divide both sides by [tex]10[/tex] in above equation as follows:
[tex]\begin{aligned}\dfrac{10x}{10}&=\dfrac{4200}{10}\\x&=420\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]420[/tex].
Thus, the amount of [tex]\$\ 20[/tex] coffee is [tex]\boxed{\bf 420\text{\bf pounds}}[/tex].
Learn more:
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2. Learn about solving equation https://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.
