Answer:
Zoe can clear tables for 7, 8 , 9 and 10 hours to meet her requirements.
Step-by-step explanation:
Here according to the question:
Earning per hour of Zoe from babysitting = $7 per hour
Earning per hour of Zoe from clearing tables = $15 per hour
Let us assume the number of hours Zoe babysits = m hours
Also, let us assume the number of hours Zoe clears table = n hours
Now,as given : She can make a maximum of 14 total hours
SO, the number of hours worked at ( Babysitting + Clearing Tables) ≤ 14
or, m + n ≤ 14 ....... (1)
Now, the total earning after working m hours babysitting
= m x ( Cost of babysitting per hour) = m ($7) = 7 m
And, the total earning after working n hours clearing tables
= n x ( Cost of clearing tables per hour) = n ($15) = 15 n
Now, total earning after worming both jobs = 7 m + 15 n
But, She can must earn at least $130.
⇔ 7 m + 15 n ≥ 130 ......... (2)
Now, given : Number of hours Zoe babysits = 4 hours
⇒ m = 4
So, putting the value of m = 4 in (1) , we get: n = 14 - 4 = 10
Also, putting m = 4, n = 10 in (2) , we get:
7 m + 15 n = 7 (4) + 15(10) = 28 + 150 = 178 > 130
Hence, (4,10) is the SOLUTION OF THE GIVEN SYSTEM.
now, m = 4, so, n can be 1, 2, 3, 4, 5, .... 9 (any of the values)
for, m = 4, n = 1: 7 m + 15 n = 28 + 15 = 43 ≯ 130
⇔ Equation (2) is not satisfied for (4,1)
Checking for all values of (m,n), we get:
The possible solutions are: (4 ,7) , (4,8) , (4,9) and (4, 10).
Hence, she can clear tables for 7, 8 , 9 and 10 hours to meet her requirements.
