Word Problems

[bryan]

I need help to understand how to set up an equation and the steps needed to comlpete to solve for a word problem.


Question:
An 18 lb mix is worth $61.20 resulted when prunes that sell for $3.20 per pound were combined with apricots that sold for $3.50 per pound. How many pounds of each type of fruit was in the mix?

 

[soroban]

Hello, bryan!

An 18-lb mix is worth $61.20 resulted when prunes that sell for $3.20 per pound
were combined with apricots that sold for $3.50 per pound.
How many pounds of each type of fruit was in the mix?

Let \(\displaystyle x\) = number of pounds of prunes.
Then \(\displaystyle 18\!-\!x\) = number of pounds of apricots.

There are: \(\displaystyle x\) pounds of prunes at \(\displaystyle $3.20\) per pound.
This is worth: \(\displaystyle 3.20x\) dollars.

There are: \(\displaystyle 18\!-\!x\) pounds of apricots at \(\displaystyle $3.50\) per pounds.
This is worth: \(\displaystyle 3.50(18-x)\) dollars.

The total value is: \(\displaystyle 3.20x + 3.50(18-x)\) dollars.

We are told that the total value is: \(\displaystyle 61.20\) dollars.

There is our equation! . . . \(\displaystyle 3.20x + 3.50(18-x) \:=\:61.20\)

Go for it!