mixture problem

[joepa3]

A shop makes a 140 bushels of a corn & oats mixture. If a bushel of oats coast 80 cents and a bushel of corn costs $1.50, How many bushels of each are needed to make a mix that sells for $1.20?

Please advise. thanks

 

[Deleted member 4993]

A shop makes a 140 bushels of a corn & oats mixture. If a bushel of oats coast 80 cents and a bushel of corn costs $1.50, How many bushels of each are needed to make a mix that sells for $1.20?

Please advise. thanks

Start with - what you got to find and name those as variables.

You need find amount of corn and amount of oats - in a 140 bushel mixture. So let

Amount of corn = C

Amount of Oats = T

We are given the total amount as 140 bushels. So:

C + T = 140 ..................................................................... (1)

What else??

 

[soroban]

Hello, joepa3!

A shop makes 140 bushels of a corn-and-oats mixture.
If a bushel of oats sells for 80 cents and a bushel of corn sells for $1.50,
how many bushels of each are needed to make a mix that sells for $1.20?

Let \(\displaystyle x\) = bushels of oats.
Let \(\displaystyle y\) = bushels of corn.

We have an equation: .\(\displaystyle x + y \:=\:140\) .[1]


\(\displaystyle x\) bushels of oats at 80 cents a bushel has a value of \(\displaystyle 0.80x\) dollars.

\(\displaystyle y\) bushels of corn at $1.50 a bushel has a value of \(\displaystyle 1.50y\) dollars.

The total value of the mixture is: .\(\displaystyle 0.80x + 1.50y\) dollars.


But we know that the mixture will be 140 bushels which sells for $1.20 a bushel.
. . Hence, the value of the mixture is: .\(\displaystyle 140(1.20) \:=\:\168\) dollars.

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

We have another equation: .\(\displaystyle 0.8x + 1.5y \:=\:168\) .[2]


We have a system of equations: .\(\displaystyle \begin{array}{ccc}x + y &=& 140 \\ 0.8x + 1.5y &=& 168 \end{array}\)

Solve the system.