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math, wage question. can you show me how to do it?

Jennys wage is $600 + 0.90 per customer served.

1) in a good week jenny wage is $1000 or more. what is the least number of customers that jenny must serve to have a good week?

2) at the same job shawn, is paid a weekly wage of $270 plus, $1.50 for each customer.
if shawn weekly wage in dollars, write a formula, for calculating weekly wage.

3) in a certain week jenny & shawn receive the same wage for the number of customers, how many customers did they each have?

Reply 1

AlexApp

1). Jenny has $600 base wage, the additional amount needed for a 'good' week is $400 ($1000 - $600). Then you work out how many customers she needs to serve to make $400 by doing $400/$0.9 = 444.44 customers. This needs to be rounded up to 445 customers.

2). Think of the total wage as a component of base wage and 'bonuses' from serving more customers:

Shawn's Total wage (SW) = $270 (base wage) + $1.50 x Number of customers (N). As an algebraic expression, SW = 270 + 1.5N
Therefore, similarly Jenny's Total Wage (JW) = $600 + $0.90 x N. i.e. JW = 600 + 0.9N

3). In this situation both earn the same wage, so we can say that Shawn's Total Wage = Jenny's Total Wage (SW = JW).

Using this fact, you can make a simultaneous equation from the answer to question 2.

Shawn's wage on the left, Jenny's on the right:
270 + 1.5N = 600 + 0.9N

Now you need to solve for N (get N on one side and the numbers on the other):
1.5N = 600 + 0.9N - 270 (-270 both sides)
1.5N - 0.9N = 600 - 270 (-0.9N both sides)
0.6N = 330
Then divide through by 0.6 to get N by itself;
N = 330/0.6
N = 550

You can then validate that 550 customers need to be served for their wages to be equal by plugging the result for N back into the equations from question 2:
Shawn: 270 + (1.5 x 550) = 1095
Jenny: 600 + (0.9 x 550) = 1095

Hopefully that helps!

(edited 5 years ago)