Question

Declan purchases a new computer with his credit card. if Declan pays the minimum monthly payment, he will have his balance paid off in 38 months versus 26 months if he pays an additional $35.00 each month. what percent of time will save by paying the extra $35.00 per month.31.57%31.58%46.15%46.16%

Answer 1

31.58%

Step-by-step explanation

we can easily solve this by using a rule of three

then

Step 1

Let x represents the percentage for 26 months, so

`\begin{gathered} \text{if} \\ 38\Rightarrow100\text{ \%} \\ \text{then} \\ 26\Rightarrow x \end{gathered}`

we can make a proportion

`(38)/(100)=(26)/(x)`

now, let's solve for x

`\begin{gathered} (38)/(100)=(26)/(x) \\ \text{cross multiply} \\ 38\cdot x=26\cdot100 \\ 38x=2600 \\ \text{divide both sides by 38} \\ (38x)/(38)=(2600)/(38) \\ x=68.42105\text{ \%} \end{gathered}`

so, the percentage for 26 months is 68.42105 %

Step 1

now, to know the percentage saved we need to do a subtraction.

so

% of time saved = 100%-(percentage for 26 months)

replace

`\begin{gathered} \text{ saved=100\%-68.42105} \\ \text{ saved=31.578947} \\ \text{rounded} \\ 31.58\text{ \%} \end{gathered}`

therefore, the answer is

31.58%

I hope this helps you