A person invested $7200 for 1 year, part at 4\%, part at 10\%, and the remainder at 15\%. The total annual income from these investments was $863. The amount of money invested at 15\% was $1400 more than the amounts invested at 4\% and 10\% combined. Find the amount invested at each rate.The person invested $__ at 4\%, $__ at 10\%, and $__ at 15\%.A person invested $7200 for 1 year, part at 4\%, part at 10\%, and the remainder at 15\%. The total annual income from these investments was $863. The amount of money invested at 15\% was $1400 more than the amounts invested at 4\% and 10\% combined. Find the amount invested at each rate.Solution –Let the amount invested at 4\% be x, amount at 10\% be y, then the amount at 15\% should be –4\% ————————– x
10\% ————————– y
15\% ————————– 7200 – (x + y)0.04x + 0.1y + 0.15 (7200 – (x + y)) = 863
0.04x + 0.1y + 0.15 (7200 – x – y) = 863
0.04x + 0.1y + 1080 – 0.15x – 0.15y = 863
0.04x – 0.15x + 0.1y – 0.15y = 863 – 1080
-0.11x – 0.05y = -217
0.11x + 0.05y = 217 — INow since the amount of money invested at 15\% was $1400 more than the amounts invested at 4\% and 10\% combined, we have –(x + y) = 7200 – (x + y) + 1400
x + y = 7200 – x – y + 1400
x + x + y + y = 7200 + 1400
2x + 2y = 8600
x + y = 8600/2
x + y = 4300 — IINow solve I and II using substitution to get the values –From II, x = 4300 – y — IIIPut this value of x in equation I, —
0.11(4300 – y) + 0.05y = 217
473 – 0.11y + 0.05y = 217
-0.06y = 217 – 473
y = -256/-0.06
y = 4266.67Now put this value of y in equation III —
x = 4300 – 4266.67
x = 33.33Amount invested at —
4\% ————————– $33.33
10\% ————————– $4266.67
15\% ————————– 7200 – (33.33 + 4266.67) = $2900
Why Choose Us
- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee
How it Works
- Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the "PAPER DETAILS" section.
- Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
- From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.