math
posted by micheal .
Review example 2 How does the author determine what the?
Example 2. Translate. The first row of the table and the fourth sentence of the
problem tell us that a total of 63 pupae was received. Thus we have one
equation: p+q=63
Since each pupa of morpho granadensis costs $4.15 and p pupae were
received, 4.15p is the cost for the morpho granadensis species. Similarly,
1.50q is the cost of the battus polydamus species. From the third row of
the table and the information in the statement of the problem, we get a
second equation: 4.15p+1.50q=147.50
We can multiply by 100 on both sides of this equation in order to clear
the decimals. This gives us the following system of equations as a
translation: p+q=63, (1)
415p+150q=14,750. (2)
Solve. We decide to use the elimination method to solve the system.
We eliminate q by multiplying equation (1) by 150 and adding it to
equation (2): 150p  150q = 9450 Multiplying equation (1) by 150
415p +150q=14,750
263p =5300 adding
p =20. solving for p
To find q, we substitute 20 for p in equation (1) and solve for q:
p+q=63 Equation (1)
20+q=63 Substituting 20 for p
q=43. Solving for q
We obtain (20,43),or p=20, q=43
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