Question

Kayla is buying fruit for packed lunches. She needs to buy an assortment of at least 15 apples and oranges and spend less than $20.00. Apples (x) cost $0.65 each, an oranges (y) cost $0.78 each. Which system of linear inequalities models this situation?

Answer 1

`\left\{\begin{array}{l}x+y\ge 15\\ \\0.65x+0.78y<20\\ \\x\ge 0\\ \\y\ge 0\end{array}\right.`

Explanation:

Let x be the number of apples and y be the number of oranges Kayla buys.

She needs to buy an assortment of at least 15 apples and oranges, then

`x+y\ge 15`

Apples cost $0.65 each, then x apples cost $0.65x

Oranges cost $0.78 each, then y oranges cost $0.78y.

She spends less than $20.00, so

`0.65x+0.78y<20`

Not that the number of apples and oranges must satisfy inequalities

`x\ge 0\\ \\y\ge 0,`

so the following system of inequalities models this situation:

`\left\{\begin{array}{l}x+y\ge 15\\ \\0.65x+0.78y<20\\ \\x\ge 0\\ \\y\ge 0\end{array}\right.`