helpp me with this math equation please?

nethead needs to have his new shocks installed in his van. he has looked into two different shops, als auto repair and jorges auto tech. they each charge an hourly rate plus a fixed cost. the cost for a 2hour job and 5hour job for each shop is given below.

al’s auto repair
2hr – $90
5hr – $195

jorges auto tech
2hr – $100
5hr – $190
write an equation relating the cost, c to the time t for als auto repair
write an equation relating the cost c to the time t for jorges auto tech
for what amount of time do the mechanics charge the same amount and what is the cost for this amount

For Al we have the following equations

Fixed(Al) + 2 x Hourly(Al) = $90
Fixed(Al) + 5 x Hourly(Al) = $195

Subtracting we see 3 x Hourly(Al) = $105
so Hourly(Al) = $35

Therefore Fixed(Al) = $20

Using there two values we see that the cost c = $20 + $35 x t

For Jorge

Fixed(Jo) + 2 x Hourly(Jo) = 100
Fixed(Jo) + 5 x Hourly(Jo) = 190

Subtracting we see 3 x Hourly(Jo) = $90
so Hourly(Jo) = $30

Therefore Fixed(Jo) = $40

Using there two values we see that the cost c = $40 + $30 x t

For some t the garages charge the same

If we equate the two equations we see that

40 + 30t = 20 + 35t for some t

t5 = 20
t = 4

So they charge the same for 4 hour jobs and when t = 4 that amount is $160

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