Question

Samuel wants to buy at least twice as many DVDs as CDs. CDs sell for $7 each, and DVDs sell for $12 each. Samuel can spend a maximum of $50. Let c represent the number of CDs, and let d represent the number of DVDs. Which system of inequalities can be used to find the number of CDs and DVDs Samuel can buy?

Answer 1

The inequalities that will be used are:

d ≥ 2c

7c+12d ≤ 50

Explanation:

Let:

c = number of CDs purchased

d = number of DVDs purchased.

It is given that:

Samuel wants to buy at least twice as many DVDs as CDs.------------(1)

CDs sell for $7 each, and DVDs sell for $12 each.

Samuel can spend a maximum of $50.-----------------(2)

Let c represent the number of CDs, and let d represent the number of DVDs.

Hence, we have from first statement that:

d ≥ 2c.

From the second statement we have:

7c+12d ≤ 50

Hence, the inequalities used are:

d ≥ 2c

7c+12d ≤ 50.

Answer 2

c = number of CDs purchased
d = number of DVDs purchased.

Sam wants to buy at least twice as many DVDs as CDs, therefore
d >= 2c (1)

Sam can spend up to $50. Each CD costs $7 and each DVD costs $12. Therefore
7c + 12d <= 50 (2)

Equations (1) and (2) represent the system of inequalities for the problem.