Question

Coach A is offering her services for an initial $6,925 in addition to $450 per hour. Coach B is offering her services for an initial $5,000 in addition to $725 per hour. When will the two coaches charge the same amount of money? The two coaches will charge the same amount of money after

Answer 1

The two coaches will charge the same amount of money after working for 11 hours

Explanation:

Let us assume for m hours, they both will charge same amount.

For COACH A:

The initial Fee = $ 6,925

The per hour fee = $450

So, the fees in m hours = m x ( Per hour fees) = m x ($450) = 450 m

So, the total fees of Coach A in m hours = Initial Fee + fee for m hours

= $ 6,925 + 450 m

⇒ The total fees of Coach A in m hours = $ 6,925 + 450 m .... (1)

For COACH B:

The initial Fee = $ 5,000

The per hour fee = $725

So, the fees in m hours = m x ( Per hour fees) = m x ($725) = 725 m

So, the total fees of Coach B in m hours = Initial Fee + fee for m hours

= $ 5,000 + 725 m

⇒ The total fees of Coach B in m hours =$ 5,000 + 725 m .... (2)

Now, for m hours , they both charge the SAME AMOUNT fees

⇒$ 6,925 + 450 m = $ 5,000 + 725 m ( from (1) and (2))

or, 6925 - 5000 = 725 m - 450 m

or, 1925 = 175 m

or,m = 1925 / 175 = 11

or, m = 11

Hence, the two coaches will charge the same amount of money after working for 11 hours.