Question

jonah is going to the store to buy candles. Small candles cost $3.50 and large candles cost $5.00. he needs to buy at least 20 candles, and he cannot spend more than $80. Write a system of linear inequalities that represent the situation.

Answer 1

Jonah needs to buy "at least" 20 candles, so he can buy 20 or more candles. Another way to say this is that the number of candles he's going to need is "greater than or equal to 20." Use S to represent small candles, and L for the large ones. The total number of candles he buys is S+ L.

 

S + L > 20

 

There's one inequality. Now we need the inequality about money. He "cannot spend more than $80." That means he's allowed to spend either exactly 80 bucks or less. In other words, the money he spends is "equal to or less than 80." Because this inequality is about money, we need to put the prices into play. The small candles cost $3.50, so use that as a coefficient for S. Large candles cost $5, so that's the coefficient for L.

 

3.50S + 5L < 80