Question

Robert is purchasing some equipment for his baseball team. He wants to buy some baseballs, each priced at m dollars. He has already spent b dollars on other equipment.
The following expression represents the total amount Robert will spend after buying x baseballs.



If the amount already spent by Robert on other equipment, b dollars, is doubled, then the value of m will ______________________.

If the cost of each baseball, m dollars, is tripled, then the value of b will_________________ and the value of mx will _______________________.

Answer 1

Answer:

1. The following expression represents the total amount Robert will spend after buying x baseballs:

• y = mx + b

2. If the amount already spent by Robert on other equipment, b dollars, is doubled, then the value of m will:

• remain the same (m)

3. If the cost of each baseball, m dollars, is tripled, then the value of b will remain the same (b) and the value of mx will be tripled (3mx)

Explanation:

1. Since the price of one baseball is m, the cost of x baseballs is m times x: mx.

Since he has already spent b dollars on other equipment, to calculate the total amount spent after buying x balls, you have to add both the value spent of other equibment (b) and the value of x balls (mx), thus the expresssion that represents the total amounf Robert will spend is:

• mx + b

2. If the amount already spent by Robert on other equipment, b dollars, is doubled, then the value of m does not change, because it is the price of each baseball, which is a constant unit price.

3. If the cost of each baseball, m dollars, is tripled, then the value of b does not change, because it is an amount calculated from the purchase of other equiment and not baseballs.

As per the value of mx, since the new price is the triple, instead of m it  will be 3m,  and you have to use 3mx instead of mx.