Video: Creating Linear Inequalities with One Variable

A candy store has a special offer; if you spend more than $15, you get a free chocolate drink. Gift boxes are $3 each, and chocolates are $2 per 50 g. Write an inequality to find 𝑀, the weight of chocolate you must buy with a gift box, if you want to receive a free chocolate drink.

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Video Transcript

A candy store has a special offer; if you spend more than 15 dollars, you get a free chocolate drink. Gift boxes are three dollars each, and chocolates are two dollars per 50 grams. Write an inequality to find 𝑀, the weight of chocolate you must buy with a gift box, if you want to receive a free chocolate drink.

We know that the special offer of a free chocolate drink happens if you spend more than 15 dollars. This means that our expression must be greater than 15. We know that one gift box costs three dollars. We also know that chocolates cost two dollars for 50 grams. Dividing both of these by two means that we can buy 25 grams of chocolate for one dollar. The weight of chocolate we need to buy is 𝑀. Therefore, the cost of this will be 𝑀 divided by 25 as each 25 grams of chocolate costs one dollar. We’re also buying one gift box which costs three dollars. This means that our total spend is 𝑀 over 25 plus three.

To receive the free gift, this must be greater than 15. The inequality to find 𝑀 is therefore 𝑀 over 25 plus three is greater than 15. Whilst we don’t need to do so in this question, we could solve the inequality by firstly subtracting three from both sides. This would give us 𝑀 over 25 is greater than 12. Our second step would be to multiply this inequality by 25. The inverse or reciprocal operation of dividing by 25 is multiplying by 25. 12 multiplied by 25 is equal to 300. This means that you would need to buy more than 300 grams of chocolate to qualify for the free chocolate drink.

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