# Manuel takes a job translating English instruction manuals to Spanish. He will receive \$15 per page plus \$100 per month. Manuel would like to work for 3 months during the summer and make at least \$1500. Please help explain how to write and solve an inequality to find the minimum number of pages Manuel must translate in order to reach his goal.

Let's review the information we know and then set up an inequality.  We know that Manuel wants to earn a minimum of \$1500 over a 3 month period.  He earns \$15 per translated page and we are trying to determine the number of pages he must translate, so let's call...

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Let's review the information we know and then set up an inequality.  We know that Manuel wants to earn a minimum of \$1500 over a 3 month period.  He earns \$15 per translated page and we are trying to determine the number of pages he must translate, so let's call the number of pages he must translate x.  If we multiply the two, then the total amount he earns from pure translating is 15x.  But he also earns an extra \$100 per month, so over three months that is \$300 that must also be taken into account (or added to 15x).  So the inequality to set up is shown below.

`15x + 300 gt= 1500`

Subtract 300 from both sides.

`15x gt= 1200`

Now divide both sides by 15.

`x gt= 80`

So he must translate at least 80 pages to make at least \$1500.

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