Using a system of equation, we have that:
a)
- x, which is the cost of on-site service.
- y, which is the cost of at-store service.
- z, which is the cost of by-mail service.
b)
The system is:
[tex]x = 3y[/tex]
[tex]z = y - 10[/tex]
[tex]15x + 40y + 5z = 3100[/tex]
c)
The cost of one on-site repair service is of $90.
Item a:
The variables are:
- x, which is the cost of on-site service.
- y, which is the cost of at-store service.
- z, which is the cost of by-mail service.
Item b:
On-site service costs 3 times as much as at-store service, thus:
[tex]x = 3y[/tex]
By mail service costs $10 less than at-store service, thus:
[tex]z = y - 10[/tex]
Last week, the shop completed 15 services on-site, 40 services at-store, and 5 services by mail for total sales of $3100, thus:
[tex]15x + 40y + 5z = 3100[/tex]
The system is:
[tex]x = 3y[/tex]
[tex]z = y - 10[/tex]
[tex]15x + 40y + 5z = 3100[/tex]
Item c:
- The cost of one on-site repair service is x.
- First, replacing the first two equations into the third, we find y, and then with it we find x.
[tex]15x + 40y + 5z = 3100[/tex]
[tex]15(4y) + 40y + 5(y - 10) = 3100[/tex]
[tex]60y + 40y + 5y = 3150[/tex]
[tex]105y = 3150[/tex]
[tex]y = \frac{3150}{105}[/tex]
[tex]y = 30[/tex]
Then
[tex]x = 3y = 3(30) = 90[/tex]
The cost of one on-site repair service is of $90.
A similar problem is given at https://brainly.com/question/24823220
