Sure, we can solve this problem using two equations based on the problem's statements.
Let's denote:
- `x` as the amount invested in account 1 (with an interest rate of 4%),
- `y` as the amount invested in account 2 (with an interest rate of 8%).
From the problem we know that the total amount invested (x + y) is $1,750. So we can write our first equation as:
1) x + y = 1750.
Since we also know that the total yield is $94, which comes from both investments (4% of x and 8% of y), we can write our second equation as:
2) 0.04x + 0.08y = 94.
So we have a system of two equations. To solve it, we can use the method of substitution or elimination.
It seems more convenient to use elimination in our case. First, let's multiply the first equation by 0.04, yielding:
0.04x + 0.04y = 70.
Now subtract this new first equation from the second one:
0.04y = 24.
Notice that we obtained an equation with one variable. Solve it for y by dividing both sides by 0.04:
y = 24 / 0.04 = 600.
Now we can find x by substituting y = 600 into the first equation:
x + 600 = 1750
x = 1750 - 600 = 1150.
So the solution of the problem is:
Helene invested $1,150 in the account offering 4% interest and $600 in the account offering 8% interest. Here both the total amount of money invested ($1,750) and the total interest earned after one year ($94) agree with the problem's statements.