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Let's call the number of minutes Rachel talked on her phone "m."
The total cost of Rachel's bill is the flat rate plus the charge per minute multiplied by the number of minutes she talked.
$5.25 + $0.29m = $27.00
Subtract $5.25 from both sides:
$0.29m = $21.75
Divide both sides by $0.29:
m = 75
Rachel talked for 75 minutes.