Chris V. answered • 08/10/16

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Engineering student with a love for math, science, and writing

Let's begin by defining our variables:

X = amount in the 5% account

Y = amount in the 7% account

Z = amount in the 8% account

With three variables, we need three equations. We will find these equations from the information in the problem. First, the easiest of them is that they total up to 1520. So if we add them all together we end up with 1520:

X + Y + Z = 1520

Next, we know that the 5% account is half of the 7% account:

X = 0.5 Y or: 2X = Y

Finally, the 7% investment is 1500 less than 8% investment:

Y = Z - 1500

So our three equations:

X + Y + Z = 1520

X = 0.5 Y

Y = Z-1500 or Z = Y+1500

Let's replace the X and Z in the first equation with the information from the second and third equations.

(0.5Y) + Y + (Y+1500) = 1520 --- Now we just add up the Ys together

2.5Y + 1500 = 1520 --- Subtract 1500 from both sides

2.5Y = 20 --- Solve for Y

*Y = 8*

So now we use Y = 8 to find the other two values.

X = (0.5Y) --> X = (0.5*8) ---> X = 4

Z = Y+1500 ---> Z = 1508.

Finally, we just test the numbers by adding them together. We should end up with 1520.

1508 + 8 + 4 = 1508 + 12 = 1520. They add up correctly and our answer is verified.

**$4 in the 5% account**

**$8 in the 7% account**

**$1508 in the 8% account**