7. bill and steve both owe their mother money. bill owes his mother $300 and plans
to pay her $25 every week. steve owes his mother $550 and plans to pay her
$75 every week. after how many weeks will they both owe their mother the same
amount of money? what amount will that be?

5 weeks

$175

Step-by-step explanation:

Bill owes his mother $300 and plans to pay her $25 every week.

Therefore, after w weeks he has to give her mother more C = 300 - 25w, amount of money.

Steve owes his mother $550 and plans to pay her  $75 every week.

Therefore, after w weeks he has to give her mother more C = 550 - 75w, amount of money.

If after w weeks they both will owe their mother the same amount of money, then  

300 - 25w = 550 - 75w

⇒ w = 5 weeks. (Answer)

Now, the amount of money will be $(300 - 25 × 5) = $175. (Answer)

both equations and proportions are better.