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. Write two possible solutions to this problem

Answer 1

`\text{Let the number of small candle Jonah bough is x and the number of }\\ \text{large candles be y.}\\ \text{He needs to buy at least 20 candles, so we have}\\ \\ x+y \geq 20\\ \\ \text{one small candle cost }\$3.50 \text{ and the large candle costs }\$5.00`

`\text{He cannot spend more than 80 dollars, so we have}\\ \\ 3.50x+5y\leq 80\\ \\ \text{so the system of inequalities that represent the situation is}\\ \\ \left\{\begin{matrix} x+y\geq 20\\3.50x+5y\leq 80   \end{matrix}\right. \\ \text{Two possible solutions to this problem are: }(18,3) \text{ and }(19,2)\\ \\ \text{that is one solution is 18 smaller candles and 3 large candles}\\ \text{and the other solution is 19 small candle and 2 large candles.}`