# math

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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
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
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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