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Jamele runs a grocery store that sells bar coffee bean blend by the pound. she wishes to mix 40 pounds of coffee to sell for a total cost of $222. to obtain the mixture she will mix coffee that sells for $5.10 per pound with coffee that sells for $6.30 per pound. how many pounds of each coffee should she use

Sagot :

As per given by the question.

There are given that total mix pounds is 40.

Now,

There is two equation would be needed, one to the acount for money and the other to account for mass.

Then,

x is the pounds of $ 5.10/pound coffee.

y is the pouns of 6.30/pound coffee.

So,

The first equation is;

[tex]5.10x+6.30y=222[/tex]

And;

The grocer wants to mixture of 40 pounds of coffee,

So;

[tex]x+y=40[/tex]

Now,

From the second equation,

[tex]\begin{gathered} x+y=40 \\ x=40-y \end{gathered}[/tex]

Then,

Put the value of x into the first equation.

So,

[tex]\begin{gathered} 5.10x+6.30y=222 \\ 5.10(40-y)+6.30y=222 \\ 204-5.10y+6.30y=222 \\ 204+1.2y=222 \\ 1.2y=18 \\ y=15 \end{gathered}[/tex]

Now,

Put the value of y into the second equation;

So,

[tex]\begin{gathered} x=40-y \\ x=40-15 \\ x=25 \end{gathered}[/tex]

Hence, the 25 and 15 pounds of each coffee shoud she use.

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