Question

Tony has $18 to buy apples and bananas for afruit salad. Apples cost $2 per pound andbananas cost $1 per pound. Write and graph aninequality to describe the situation. Then givetwo possible combinations of pounds of applesand bananas that Tony can buy.

Answer 1

a is the number of pounds of apples

b is the number of pounds of bananas

Apples cost: 2a

Bananas cost: b

As Tony has $18 to buy apples and bananas the inequality that represents the situation is:

`2a+b\leq18`

To graph it:

1. Identify the equation of the boundary line:

`2a+b=18`

2. Find two ordered pairs:

Find b when a is 1:

`\begin{gathered} 2(1)+b=18 \\ 2+b=18 \\ b=18-2 \\ b=16 \end{gathered}`

Ordered pair: (1,16)

Find b when a is 3:

`\begin{gathered} 2(3)+b=18 \\ 6+b=18 \\ b=18-6 \\ b=12 \end{gathered}`

Ordered pair: (3,12)

2. Use the ordered pairs to draw the boundary line, as the inequality sing is less than or equal to shadow area is under the line:

The possible combinations of pound of apples and bananas are those combinations that fits in the shadow area.