Algebra 5.4 solving systems of linear equations

Question

A small bag of trail mix contains 3 cups of dried fruit and 4 cups of almonds. A large bag contains 4 1/2 cups of dried fruit and 6 cups of almonds. Write and solve a system of linear equations to find the price of 1 cup of dried fruit and 1 cup of almonds. Let f represent the price of one cup of dried fruit and let a represent the price of one cup of almonds.

Answer 1

Hi Ella B.,

So, what this question essentially askes yo to do is, generate two equations that use the variables f and a and that describe how much each bag type of trail mix costs.

So, you just plug the unit prices (prices per cup), times the quantitites of each in bag of trail mix.

That would be:

$small = 3f + 4a

$large = 4.5f + 6a

But, you can't solve to get number values for each commodity, unless you have values for $small and $large.

If you lack these values, you can still solve for f and a in terms of the variables $small and $large, by eliminating variables from the two equations. You have two possible methods for that, elimination and substitution; you SHOULD know how to do that?

-- Cheers, --Mr. d.