Systems of Linear Equations with Infinitely Many Solutions
John
| \
| \
|. \
|. \
(a)400ft
|. \
|. \
|. \(c) length of rope
|. \
|. \
|____________________Boat
350 ft (b)
Pythagorean theorem
a-squared + b-squared = c-squared
400-squared + 350-squared = c-squared
160,000 + 122,500 = c- squared
282,500 = c-squared
Now take the square root of each side of the equation
531.5 = c
The length of the rope is 531.5 feet
Answer: Part-to-part
Step-by-step explanation:
This is a part-to-part, because they show part of apples, and part of oranges. This ratio when set up is 4:3. If the ratio was part-to-whole, then the apples would be compared to the total amount of oranges and apples. The ratio for part-to-whole would be 4:7.
Hope this helps!
499.50 is the total amount of discounts given to senior citizens
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
==================
Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%