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kherson [118]
3 years ago
15

A small bag of trail mix contains 3 cups of dried fruit and 4 cups of almonds.A large bag contains 41/2 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 if the Price of small bag is $6 while $9 for large bag.  
      
Mathematics
1 answer:
Juliette [100K]3 years ago
3 0
Let's call:
f = price of 1 cup of dried fruit
a = price of 1 cup of almonds

In order to build the linear system, you need to consider that the total price of a bag is given by the sum of the price of cups times the number of cups in each bag, therefore:

\left \{ {{3f + 4a = 6} \atop {41/2 f + 6a = 9 }} \right.

Solve for a in first equation:
a = (6 - 3f) / 4

Then substitute in the second equation:
41/2 f + 6 · (6 - 3f) / <span>4 = 9
41/2 f + 9 - 9/2 f = 9
16 f = 0
f = 0

Now, substitute this value in the formula found for a:
</span>a = (6 - 3·0) / <span>4
   = 3/2 = 1.5

Hence, the cups of dried fruit are free and 1 cup of almond costs 1.5$</span>

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