A total of 23,456.78 dollars was invested in two funds paying 2½ percent and 1¾ annual interest. The combined interest for the year percent is 368 dollars and 50 cents.

Question

A total of 23,456.78 dollars was invested in two funds paying 2½ percent and 1¾ annual interest. The combined interest for the year percent is 368 dollars and 50 cents.

Part A: How much of the 23,456.78 dollars is invested in 2½ percent fund?
Part B: How much of the 23,456.78 dollars is invested in 1¾ percent fund?

Answer 1

let x be the amount invested at 2½%

Then the rest (23456.78-x) was invested at 1¾%

So now, just add up the interest to find x.
0.025x + 0.175(23456.78-x) = 368.50

once you have x, you know the two amounts.

Answer 2

To solve this problem, we can use a system of equations. Let's denote the amount invested in the 2½ percent fund as 'x' and the amount invested in the 1¾ percent fund as 'y'.

Part A: We know that the total amount invested is $23,456.78, so we can write the equation:

x + y = 23,456.78

Part B: We are also given the combined interest for the year, which is $368.50. The interest earned from the 2½ percent fund is calculated by multiplying the amount invested by the interest rate (2.5%) and dividing by 100. Similarly, the interest earned from the 1¾ percent fund is calculated by multiplying the amount invested by the interest rate (1.75%) and dividing by 100. So, we can write the equation:

0.025x + 0.0175y = 368.50

Now, we can solve this system of equations to find the values of 'x' and 'y'.

One way to solve this system of equations is by substitution. Rearrange the first equation to solve for 'x':

x = 23,456.78 - y

Substitute this expression for 'x' into the second equation:

0.025(23,456.78 - y) + 0.0175y = 368.50

Now we can solve for 'y':

586.42 - 0.025y + 0.0175y = 368.50
0.0175y - 0.025y = 368.50 - 586.42
-0.0075y = -217.92
y = (-217.92) / (-0.0075)
y = 29,056

Now substitute this value of 'y' back into the first equation to find 'x':

x + 29,056 = 23,456.78
x = 23,456.78 - 29,056
x = -5,599.22

Since it doesn't make sense to have a negative amount invested, we can conclude that there must have been a mistake or omission in the problem. Please double-check the given information or verify that no additional details were provided.