Q4. - Algebra 1

Question

Carolyn has 9 quarters, 4 dimes, 7 nickels and 2 pennies, which can be represented as in below:

$\mathbf{9}\left(25\right)\mathbf{+}\mathbf{4}\left(10\right)\mathbf{+}\mathbf{7}\left(5\right)\mathbf{+}\mathbf{2}$

Evaluate the above expression to find how much money she has. Name the property used in each step:

Step-by-Step Solution

Answer

The value of the expression is: .$\mathbf{5}\left(14-5\right)\mathbf{+}\mathbf{6}\left(3+7\right)\mathbf{=}\mathbf{302}$

Step 1 – Given information.

Given expression is:

$9\left(25\right)+4\left(10\right)+7\left(5\right)+2$

Step 2 – Write the concept.

The substitution property for multiplication, addition and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a\pm b=c\end{array}$

Step 3 – Evaluate the expression.

The expression $9\left(25\right)+4\left(10\right)+7\left(5\right)+2$ can be solved in below: 

$\begin{array}{c}9\left(25\right)+4\left(10\right)+7\left(5\right)+2=225+40+35+2\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(225+40\right)+\left(35+2\right)\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =265+37\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =302\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$