Question
How would you write a realworld problem that models the
following equation:
?
(1 point)
0.08x = 0.06x + 140
A certain sum yields
$140 more in interest
when the interest rate
is 8% than when it is
6%.
On one specific item,
6% sales tax plus 8%
sales tax on the same
item adds to $140.
In a sports league, 6%
of the players times
8% of the players in
the same league
equals 140.
For a certain sum, 8%
equals $140.06.
following equation:
?
(1 point)
0.08x = 0.06x + 140
A certain sum yields
$140 more in interest
when the interest rate
is 8% than when it is
6%.
On one specific item,
6% sales tax plus 8%
sales tax on the same
item adds to $140.
In a sports league, 6%
of the players times
8% of the players in
the same league
equals 140.
For a certain sum, 8%
equals $140.06.
Answers
GPT-4o mini
The equation \(0.08x = 0.06x + 140\) can be interpreted as a real-world problem involving interest rates. Here's how you could frame it:
**Problem:**
Jack deposited a certain amount of money in a bank account that pays an interest rate of 8% per year. At the same time, he also invested a portion of that amount in a different account that earns 6% interest per year. After one year, the interest earned from the 8% account was $140 more than the interest earned from the 6% account. How much money did Jack initially deposit in total?
In this scenario:
- Let \(x\) be the total amount of money Jack initially deposited.
- The interest from the 8% account is \(0.08x\).
- The interest from the 6% account is \(0.06x\).
- The equation \(0.08x = 0.06x + 140\) represents the relationship between the interests from both accounts.
This setup clearly illustrates the given equation as a real-world problem about finance and interest rates.
**Problem:**
Jack deposited a certain amount of money in a bank account that pays an interest rate of 8% per year. At the same time, he also invested a portion of that amount in a different account that earns 6% interest per year. After one year, the interest earned from the 8% account was $140 more than the interest earned from the 6% account. How much money did Jack initially deposit in total?
In this scenario:
- Let \(x\) be the total amount of money Jack initially deposited.
- The interest from the 8% account is \(0.08x\).
- The interest from the 6% account is \(0.06x\).
- The equation \(0.08x = 0.06x + 140\) represents the relationship between the interests from both accounts.
This setup clearly illustrates the given equation as a real-world problem about finance and interest rates.