Answer:"Olivia is saving money in two different bank accounts. In the first account, she earns 1.25 times the amount of money she has in the account. In the second account, she earns 0.75 times the amount of money she has in the account. If the amount of money in the second account is $50 more than the amount in the first account, how much money does Olivia have in each account?"
Explanation:
"Olivia is saving money in two different bank accounts. In the first account, she earns 1.25 times the amount of money she has in the account. In the second account, she earns 0.75 times the amount of money she has in the account. If the amount of money in the second account is $50 more than the amount in the first account, how much money does Olivia have in each account?"
To solve this problem, we can assign variables to the amounts of money in each account. Let's say x represents the amount of money in the first account.
1.25x represents the amount of money Olivia earns in interest from the first account.
0.75x represents the amount of money Olivia earns in interest from the second account.
The equation 1.25x = 0.75x + 50 models the situation where the amount of money earned from the first account is equal to the amount earned from the second account plus $50.
To solve the equation, we can simplify it:
1.25x - 0.75x = 50
0.5x = 50
Now we can isolate x by dividing both sides of the equation by 0.5:
x = 50 ÷ 0.5
x = 100
Therefore, Olivia has $100 in the first account.
To find the amount of money in the second account, we can substitute the value of x back into the equation:
0.75x + 50 = 0.75(100) + 50
0.75x + 50 = 75 + 50
0.75x + 50 = 125
Therefore, Olivia has $125 in the second account.
In conclusion, Olivia has $100 in the first account and $125 in the second account.