Question

Anika wants to determine The maximum number of tulip bulbs (T) she can purchase if each bulb costs $1.50. She will also need to purchase separate pots for each bulb at $1.25 each and a bag of potting soil for $10. Set up an inequality to determine how many tulip bulbs Anika can purchase without spending more than $20, and solve it. Can Anika by exactly enough bulbs in pots to spend the full $20 explain can you think of a better inequality to describe the answer

Answer 1

The correct inequality is:

1.50T + 1.25T + 10 ≤ 20

The correct solution is:

T ≤ 3; no, she cannot spend the entire $20.

Explanation:

T is the number of tulip bulbs she buys. Each bulb costs $1.50; this gives the expression 1.50T.

She will buy the same number of pots as bulbs, since she needs a pot for each bulb. Each pot is $1.25; this gives the expression 1.25T.

Adding the $10 for potting soil to this, we have 1.50T+1.25T+10. She can spend no more than $20; this means she can spend less than or equal to 20. This gives us the inequality:

1.50T+1.25T+10 ≤ 20

To solve this, first combine like terms:

2.75T + 10 ≤ 20

Subtract 10 from each side:

2.75T+10-10 ≤ 20-10

2.75T ≤ 10

Divide each side by 2.75:

2.75T/2.75 ≤ 10/2.75

T ≤ 3.64

She cannot buy a partial bulb or pot, so the answer is then T ≤ 3. If she buys the same number of pots as she does bulbs, there is no way she can spend the entire $20.

Answer 2

T( 1.50+ 1.25) + 10.00 < 20.00 2.75t + 10.00 < 20.00 2.75t < 10.00 T < 3.63 Partial bulbs and puts can't be bought, so Anika cannot spent the full $20.00. Therefore, t < 3 if t can be a whole number.