Answer:To determine how much Mr. Jones invested at each rate, we can set up a system of equations based on the given information:
Let x represent the amount invested at 5%.
Let y represent the amount invested at 8%.
1) We know that the total amount invested is $18,000:
x + y = 18000
2) We also know that the amount invested at 5% and the amount invested at 8% must add up to the total amount invested:
0.05x + 0.08y = 18000
To solve this system of equations, we can use substitution or elimination. In this case, elimination is a more straightforward method.
Multiplying the first equation by 0.05 (to match the coefficient of x in the second equation), we get:
0.05x + 0.05y = 0.05 * 18000
0.05x + 0.08y = 18000
By subtracting the first equation from the second equation, we can eliminate x:
0.08y - 0.05y = 18000 - (0.05 * 18000)
0.03y = 18000 - 900
0.03y = 17100
Dividing both sides of the equation by 0.03, we find:
y = 5700
Substituting this value of y into the first equation, we can solve for x:
x + 5700 = 18000
x = 18000 - 5700
x = 12300
Therefore, Mr. Jones invested $12,300 at 5% and $5,700 at 8%.
Step-by-step explanation:
