The problem states that the cost to mail a package is $5.00. Noah has postcard stamps worth $0.34 each and first-class stamps worth $0.49 each. a. We need to write an equation that relates the number of postcard stamps $p$, the number of first-class stamps $f$, and the cost of mailing the package. b. We need to solve the equation for $f$. c. We need to solve the equation for $p$. d. If Noah puts 7 first-class stamps on the package, we need to find out how many postcard stamps he will need.

1. Problem Description

The problem states that the cost to mail a package is $5.

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0. Noah has postcard stamps worth $0.34 each and first-class stamps worth $0.49 each.

a. We need to write an equation that relates the number of postcard stamps $p$, the number of first-class stamps $f$, and the cost of mailing the package.

b. We need to solve the equation for $f$.

c. We need to solve the equation for $p$.

d. If Noah puts 7 first-class stamps on the package, we need to find out how many postcard stamps he will need.

2. Solution Steps

a. The equation that relates the number of postcard stamps $p$, the number of first-class stamps $f$, and the cost of mailing the package is:

$0.34p + 0.49f = 5.00$

b. To solve the equation for $f$, we need to isolate $f$:

$0.49f = 5.00 - 0.34p$

$f = \frac{5.00 - 0.34p}{0.49}$

c. To solve the equation for $p$, we need to isolate $p$:

$0.34p = 5.00 - 0.49f$

$p = \frac{5.00 - 0.49f}{0.34}$

d. If Noah puts 7 first-class stamps on the package, then $f = 7$. We need to find $p$.

$p = \frac{5.00 - 0.49(7)}{0.34}$

$p = \frac{5.00 - 3.43}{0.34}$

$p = \frac{1.57}{0.34}$

$p \approx 4.6176$

Since Noah cannot use a fraction of a stamp, he will need 5 postcard stamps to cover the remaining cost. Let's calculate the exact cost with $f=7$ and $p=5$:

$0.34(5) + 0.49(7) = 1.70 + 3.43 = 5.13$

So, using 7 first-class stamps and 5 postcard stamps will cost $5.13, which is more than$5.

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0. Let's try with $p=4$:

$0.34(4) + 0.49(7) = 1.36 + 3.43 = 4.79$.

The package requires $5.

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0. So, using 7 first-class stamps and 4 postcard stamps covers only $4.79, which is less than $5.

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0. This confirms that the number of postcard stamps required is

5. So the number of postcard stamps will need to be rounded to the nearest whole number. We round up because he will need enough stamps to cover the $5.

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3. Final Answer

a. $0.34p + 0.49f = 5.00$

b. $f = \frac{5.00 - 0.34p}{0.49}$

c. $p = \frac{5.00 - 0.49f}{0.34}$

d. 5