Question

0.49f + 0.34p = 5.00 solve for f and p

Answer 1

Since the total cost must be $5, the we have the following equation which relates the postacard and first class staps:

$0.49f+0.34p=5$

where f denotes the number of first class stamps and p the nunber of postcard stamps.

Now, we need to solve for f. Then, by moving 0.34p to the right hand side, we have

$0.49f=5-0.34p$

and by dividing both sides by 0.49, we get

$f=\frac{5}{0.49}-\frac{0.34}{0.49}p$

or equivalently

$f=\frac{5-0.34p}{0.49}$

Now, we need to solve for p. Then, by moving 0.49f to the right hand side, we obtain

$0.34p=5-0.49f$

and by dividing both sides by 0.34, we get

$p=\frac{5-0.49f}{0.34}$

Finally, we have that f=7 and we need to find p. In this regard, this last equation must help us. By substituting f=7, we have

$p=\frac{5-0.49(7)}{0.34}$

which gives

$\begin{gathered} p=\frac{5-3.43}{0.34} \\ p=\frac{1.57}{0.34} \\ p=4.617 \end{gathered}$

By rounding up this result, the number of postcard stamp is 5.

In summary, the answers are

$\begin{gathered} f=\frac{5-0.34p}{0.49} \\ p=\frac{5-0.49f}{0.34} \\ \text{and} \\ 5\text{ postcard stamps} \end{gathered}$