Chapter 8.4, Problem 29IP

To determine

For how many additional months will aiden need to save .

Answer to Problem 29IP

  $16\text{months}$

Explanation of Solution

Given:

Aiden has saved $85 per month for the past 7 months. He plans to save the same amount each month in the future until he has saved a total of $1955 for a new computer.

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• 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 for how many additional months will aiden need to save, let m be the additional months, first adding the past months that is 7 and the additional months and then multiplying it by 85 because he saved $85 per month, then the equation is equal to $1955 he plans to save same amount each month in the future until he has saved a total of $1955, so the equation is as shown below:

  $85(7+m)=1955$

Now, to solving the equation first using distributive property on left side of the equation and then isolate the variable term m on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate m on left side, first subtract 595 from both sides and then divide both sides by 85 and then simplify further as shown below,

  $\begin{array}{l}85(7+m)=1955\\ 85\cdot 7+85\cdot m=1955\\ 595+85m=1955\\ 595-595+85m=1955-595\\ 85m=1360\\ \frac{85m}{85}=\frac{1360}{85}\\ m=16\end{array}$

So, Aiden needs 16 months to save the money.