Question

Tara opened a savings account with $100. She saved $25 per month. Write an inequality to show thenumber of months it would take Tara to save more than $700.

Answer 1

Let x be the number of months that Tara saves the money.

The expression for the money saved after x months will be:

`100+25x`

Since we want to know when this amount saved is greater than $700, the inequality is the following:

`100+25x>700`

Remember that to solve an inequality, we proceed as if it were an equality. The only difference is that we have to be extra careful when we divide or multiply both sides of the inequality by any number, because if we divide or multiply by a negative number we turn the inequality around.

Now, let's solve or inequality step by step:

`100+25x>700\rightarrow25x>700-100\rightarrow25x>600`

Now, we need to divide both sides by 25. As it is a positive number, our inequality remains the same.

`\begin{gathered} 25x>600\rightarrow(25x)/(25)>(600)/(25)\rightarrow x>24 \\ \\ \Rightarrow x>24 \end{gathered}`

Thereby, we can conclude that Tara has to save money for more than 24 months in order to save more than $700