Question

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?

Answer 1

Bill and Steve will both owe their mother the same amount of money after 5 weeks, which will be $175 each.

Step-by-step explanation:

To find out after how many weeks Bill and Steve will both owe their mother the same amount of money, we can set up an equation where the amount Bill owes decreases by $25 each week and the amount Steve owes decreases by $75 each week.

Step-by-Step Solution:

Let w be the number of weeks after which they will owe the same amount.

Bill's debt after w weeks is $300 - $25w.

Steve's debt after w weeks is $550 - $75w.

Set the expressions equal to each other to find w: $300 - $25w = $550 - $75w.

1. Solve for w: Add $75w to both sides to get $50w = $250.
2. Divide by $50 to find w: w = 5 weeks.
3. To find out the amount they both will owe, substitute w back into either equation: $300 - $25(5) = $175.

After 5 weeks, they will both owe $175.

Answer 2

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)