Question

The Nuthouse offers a mixture of soy nuts and almonds, Almonds
sell for $7 per pound and soy nuts sell for $5.50 per pound. The
Nuthouse will make 20 pounds of the mixed nuts and sell the
mixture for $5.95 per pound. The following equations represent
the problem of keeping the cost of the mixture consistent with
the ingredients.
x + y = 20.
7x + 5.5y = 119.
x = pounds of almonds and y = pounds of soy nuts.
How many pounds of soy nuts should be used in the mixture?

URGENT!!!

Answer 1

Answer:

  14 pounds

Step-by-step explanation:

The given equations can be solved for y by substituting for x. The first equation is convenient for writing x in terms of y.

Solution

  x = 20 -y . . . . . . . subtract y from the first equation

  7(20 -y) +5.5y = 119 . . . . . substitute for x in the second equation

  140 -1.5y = 119 . . . . . . . . simplify

  21 = 1.5y . . . . . . . . . . . add 1.5y -119 to both sides

  14 = y . . . . . . . . . . . .divide by 1.5

14 pounds of soy nuts should be used in the mixture.

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Additional comment

There are many ways to solve a system of two linear equations. The attachments shows a matrix solution using a suitable calculator. It tells us that x=6 and y=14, as we found above.