Video: Writing Linear Inequalities to Represent Real-Life Situations

Michael wants to purchase a precision balance of $340. He already has $113 saved and can save $28 per week. Write an inequality that can be used to determine the number of weeks left for Michael to save at least $340.

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Video Transcript

Michael wants to purchase a precision balance of 340 dollars. He already has 113 dollars saved and can save 28 dollars per week. Write an inequality that can be used to determine the number of weeks left for Michael to save at least 340 dollars.

We will let 𝑥 equal the number of weeks. As Michael can save 28 dollars per week, the amount of money that he can save over a longer period of time will be 28 multiplied by 𝑥, which we can write as 28𝑥. Michael has already saved 113 dollars, so we can add this to our 28𝑥.

As Michael needs to save at least 340 dollars, we are going to use the greater than or equal to or more than or equal to sign. And the amount of money he wants to save is 340 dollars. Therefore our equation, our inequality, is 28𝑥 plus 113 is more than or equal to 340.

Whilst we’re not asked to work out the value of 𝑥 in this particular question, I’ll go through that process for you now. To solve an inequality, we treat it in exactly the same way as an equation and use the balancing method.

Our first step would be to subtract 113 from both sides of the equation. This would leave us with 28𝑥 is more than or equal to 227. Dividing both sides of the equation by 28 leaves us with 𝑥 is more than or equal to 8.107. As the number of weeks can only be a whole number or an integer value, we know that the number of weeks that Michael would need to save for is nine weeks.

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