Word Problem set as an inequality... Please help! :*(

[corona]

I am having trouble writing an equation for this word problem using an inequality (< or >). :(

Can anyone please help with this word problem?

Rick's Automotive charges $50 plus $15 for each (15-min) unit of time when making a road call. Twin City Repair charges $70 plus $10 for each unit of time. Under what circumstances would it be more economical for a motorist to call Rick's?

Any suggestions?

[tkhunny]

I am having trouble writing an equation for this word problem using an inequality (< or >). :(

Can anyone please help with this word problem?

Rick's Automotive charges $50 plus $15 for each (15-min) unit of time when making a road call. Twin City Repair charges $70 plus $10 for each unit of time. Under what circumstances would it be more economical for a motorist to call Rick's?

Any suggestions?Always suggestions.

U = Units of time needed
Rick = What Rick Charges = $50 + $15*U
Twin = What Twin Charges = $70 + $10*U

We're interested in using Rick, so we want to know when Twin costs more.

$70 + $10*U > $50 + $15*U

Can you finish?

[corona]

$70 + $10(u) > $50 + $15(u)

$20 > $5(u)

4 > u

Which would be 1 hour.

Thank you so much for your help!

[tkhunny]

4 > u

Which would be 1 hour.I'm a little worried about your conclusion. It's an INequality and you concluded Equality in your final statement.

What you have is u < 4, so time requirements less than one hour are what we seek. At exactly one hour, there is no difference in price. Over one hour, Rick starts getting expensive.