Chapter 1, Problem 33CR

To determine

What are the coins in her pocket.

Answer to Problem 33CR

  $\begin{array}{l}4\text{quarters }\\ \text{10 penny}\end{array}$

Explanation of Solution

Given information:

Mia has 14 coins in her pocket that total is $1.10.

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the coins in her pocket, let there are x penny and y quarter then the equation is

  $\begin{array}{l}0.01x+0.25y=1.10,\text{equation 1}\\ x+y=14,\text{equation 2}\end{array}$

Because penny is 1 cent and quarter is 25 cent in united state.

Now, solving the two equations, first putting the value of x from equation 2 to in equation 1, then subtract 0.14 from both sides and then divide both sides by 0.24, to simplify further as shown below:

  $\begin{array}{l}0.01x+0.25y=1.10,\text{equation 1}\\ x+y=14,\text{equation 2}\\ x=14-y\\ 0.01\left(14-y\right)+0.25\left(y\right)=1.10\\ 0.14-0.01y+0.25y=1.10\\ 0.14+0.24y=1.10\\ 0.14-0.14+0.24y=1.10-0.14\\ 0.24y=0.96\\ \frac{0.24y}{0.24}=\frac{0.96}{0.24}\\ y=4\end{array}$

Now putting the value of y in equation 2 to solve the value of x after putting the value of y then subtract 2 from both sides to simplify further as shown below:

  $\begin{array}{l}x+y=14,\text{equation 2}\\ y=2\\ x+2=14\\ x+2-2=14-2\\ x=12\end{array}$

So, there are 4 quarters and 10 penny in her pocket.