Chapter 0, Problem 1PR

To determine

To find:

Use any problem-solving strategy to solve each problem.

Suppose stamps for postcards cost $0.28 and stamps for first-class letters cost $0.44. Diego wanted to send postcards and letters to 10 friends. If he had $3.60 for stamps and spends all of it, how many postcards and how many letters could he send?

Answer to Problem 1PR

Explanation of Solution

Given:

Calculation:

Assign variables for the unknown values. Let x be the number of postcards and y be the number of letters. Write a system of equations for the given situation.

  $\begin{array}{l}0.28x+0.44y=3.60\\ x+y=10\end{array}$

Use $x+y=10$ to isolate x in order to perform substitution.

$x+y=10$   Write the second equation

$x+y-y=10-y$   Subtract y from both sides

$x=10-y$   Simplify

Use $x=10-y$ and perform substitution method for the first equation.

  $0.28x+0.44y=3.60$   Write the first equation

  $0.28\left(10-y\right)+0.44y=3.60$   Substitute the value of x

  $0.28-0.28y+0.44y=3.60$   Use distributive property

  $0.28+0.16y=3.60$   Combine like terms

  $0.28+0.16y-2.8=3.60-2.8$   Subtract 2.8 from both sides

  $0.16y=0.8$   Simplify

  $\frac{0.16y}{0.16}=\frac{0.8}{0.16}$   Divide both sides by 0.16

  $y=5$   Simplify

Since the value of y is known, substitute this to the second equation to determine the value of x.

  $x+y=10$   Write the second equation

  $x+5=10$   Substitute the value of y

  $x+5-5=10-5$   Subtract 5 from both sides

  $x=5$   Simplify

Diego can send 5 postcards and 5 letters.

Conclusion:

5 postcards and 5 letters