You have $45 in an account and you are saving $15 per week. Your friend has $24 in an account and is saving $18 per week. After how many weeks will you both have the same amount of money in your accounts?

Question

Savannah Anderson · Accepted Answer

7 weeks

Let the number of weeks we are looking for be #x#. The friends make a payment each week. At some stage the two amounts will be equal. We can write an equation. #24 + 18x = 45 + 15x # #18x - 15x = 45-24# #3x = 21# #x = 7# week. Or, we could figure that the difference in the accounts is reduced by $3 per week because one friend pays in $18 and the other only$15. At this rate, how long would it take to sort out the difference between $45 and $24 which is $21. #21/3 = 7 #weeks

Eli Assouline · Answer

undefined To find out when you and your friend will have the same amount of money in your accounts, we can set up an equation based on the amount of money you both have.

Let $ x $ represent the number of weeks.

For you:
Initial amount = $45
Weekly savings = $15
Total amount after $ x $ weeks = $ 45 + 15x $

For your friend:
Initial amount = $24
Weekly savings = $18
Total amount after $ x $ weeks = $ 24 + 18x $

To find when you both have the same amount of money, we set these expressions equal to each other:

$$ 45 + 15x = 24 + 18x $$

Now, solve for $ x $:

$$ 45 + 15x = 24 + 18x $$
$$ 15x - 18x = 24 - 45 $$
$$ -3x = -21 $$
$$ x = 7 $$

After 7 weeks, you and your friend will have the same amount of money in your accounts.