Question

Taylor has $900 in savings and she spends $100 each month of it on car insurance. Danny has $1200 a month but spends $150 a month on car insurance. Assuming they don't put more money into their account, do they ever have the same amount of money in their accounts, it so, when? Who runs out of money first?

Answer 1

Answer: Taylor will run out of money first after 9 months, while Danny will run out of money after 8 months.

Explanation:

To solve this problem, we can set up two equations to represent Taylor and Danny's savings over time, where x is the number of months that have passed:

Taylor: 900 - 100x

Danny: 1200 - 150x

To find out when they have the same amount of money in their accounts, we can set the two equations equal to each other and solve for x:

900 - 100x = 1200 - 150x

50x = 300

x = 6

Therefore, Taylor and Danny will have the same amount of money in their accounts after 6 months. To find out how much money they will have at that time, we can substitute x = 6 into either equation:

Taylor: 900 - 100(6) = 300

Danny: 1200 - 150(6) = 300

So after 6 months, both Taylor and Danny will have $300 in their accounts.

To determine who runs out of money first, we can set each equation equal to zero and solve for x:

Taylor: 900 - 100x = 0

x = 9

Danny: 1200 - 150x = 0

x = 8

Therefore, Taylor will run out of money first after 9 months, while Danny will run out of money after 8 months.