Mr Joyce invested $ 25,000, part at 4% interest and the remainder at 7% interest. The total income he received from his investment was $1,450. How much did he invest at each interest rate?
Thank you
if x is at 4%, then the rest (25000-x) is at 7%
So, add up the interest:
.04x + .07(25000-x) = 1450
Thank you so much Steve
To solve this problem, we can use a system of equations. Let's denote the amount invested at 4% interest as "x" and the amount invested at 7% interest as "25,000 - x" (since the total amount invested is $25,000).
We can set up two equations based on the given information:
Equation 1: 0.04x (the income from the amount invested at 4% interest)
Equation 2: 0.07(25,000 - x) (the income from the amount invested at 7% interest)
According to the problem, the total income Mr. Joyce received is $1,450, so we can set up the following equation:
Equation 3: 0.04x + 0.07(25,000 - x) = 1,450
Now, let's solve this equation step-by-step:
Step 1: Distribute the 0.07 to the terms inside the parentheses:
0.04x + 0.07 * 25,000 - 0.07x = 1,450
Step 2: Simplify the expression by multiplying:
0.04x + 1,750 - 0.07x = 1,450
Step 3: Combine like terms (x terms):
-0.03x + 1,750 = 1,450
Step 4: Subtract 1,750 from both sides:
-0.03x = 1,450 - 1,750
Step 5: Simplify the right side of the equation:
-0.03x = -300
Step 6: Divide both sides by -0.03 to solve for x:
x = -300 / -0.03
x = 10,000
Now that we have the value of x (amount invested at 4% interest), we can substitute it back into one of the original equations to find the amount invested at 7% interest:
25,000 - x = 25,000 - 10,000
25,000 - x = 15,000
Therefore, Mr. Joyce invested $10,000 at 4% interest and $15,000 at 7% interest.
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that Mr. Joyce invested an amount A at 4% interest and the remaining amount B at 7% interest.
1. The total investment amount is $25,000, so we can write the first equation as:
A + B = 25000
2. The total income from the investment is $1,450, so we can write the second equation as:
0.04A + 0.07B = 1450
Now, we can use these two equations to find the values of A and B.
There are several ways to solve this system of equations, but in this case, I will use the substitution method.
From the first equation, we can rearrange it to solve for A:
A = 25000 - B
Next, substitute this value of A into the second equation:
0.04(25000 - B) + 0.07B = 1450
Simplify and solve the equation:
1000 - 0.04B + 0.07B = 1450
0.03B = 450
B = 15000
Now that we know the value of B, we can substitute it back into the first equation to find A:
A + 15000 = 25000
A = 10000
Therefore, Mr. Joyce invested $10,000 at 4% interest and $15,000 at 7% interest.