Word Problems

[Shinymath]

Can anyone please help me with this problem.

Brian has a 4 pounds of brands 177 nuts that sell for $3 a pound. He also has brands 466 nuts that sell for $1.74 a pound. If he wants a mixture of nuts that sell for $2.30 a pound, how many pounds of brands 466 nuts should he add.




Thanks in advance

 

[soroban]

Hello, Shinymath!

Those extra numbers are annoying.

Brian has a 4 pounds of brand A nuts that sell for $3 a pound.
He also has brand B nuts that sell for $1.74 a pound.
If he wants a mixture of nuts that sell for $2.30 a pound,
how many pounds of brands B nuts should he add.?

This is the way I talk my way through these Mixture Problems . . .

We have 4 lbs of brand A at $3 per lb.
Their value is: .\(\displaystyle 4 \times 3 \:=\:12\) dollars.

We add \(\displaystyle x\) lbs of brand B at $1.74 per lb.
Their value is: .\(\displaystyle x \times 1.74 \:=\:1.74x\) dollars.

The total value of the mixture is: .\(\displaystyle 12 + 1.74x\) dollars. .[1]


The mixture will be \(\displaystyle 4+x\) lbs of nuts worth $2.30 per lb.
Its value is: .\(\displaystyle 2.30(4+x)\) dollars. .[2]


We just described the value of the mixture in two ways.

There is our equation! . . . \(\displaystyle 12 + 1.74x \:=\:2.30(4+x)\)

Got it?

 

[Shinymath]

Word Problem

Thank-you for helping me.