A line that is parallel to a side and intersects the other two siddes divides the sides proportionally.
Set up the proportion
2/x+1 = x/x+6
Multiply means and extremes
2x+12= x^2+ x
Solve to get your answer.
The numbers of new CDs is 30 and the old CDs is 21.
To solve this problem, we have to write a system of equations in which we would know the numbers of each types of CD she bought.
<h3>System of Equations</h3>
This is used to solve a series or complex of word problems in which we can represent in a mathematical statements;
- Let n represents numbers of new CDs
- Let u represents numbers of old CDs
The equations can be represented as
![n + u = 51 ...equation(i)\\15n + 6u = 576 ... equation(ii)](https://tex.z-dn.net/?f=n%20%2B%20u%20%3D%2051%20...equation%28i%29%5C%5C15n%20%2B%206u%20%3D%20576%20...%20equation%28ii%29)
Let's take equation (i)
Making n the subject of formula
![n + u = 51\\n = 51 - u...equation(iii)](https://tex.z-dn.net/?f=n%20%2B%20u%20%3D%2051%5C%5Cn%20%3D%2051%20-%20u...equation%28iii%29)
we can put equation (iii) into equation (ii)
![15n + 6u =576\\n = 51 - u\\15(51 - u) + 6u = 576\\765-15u + 6u = 576\\collect like terms\\765-576=15u - 6u\\189=9u\\9u/9 = 189/9\\u = 21](https://tex.z-dn.net/?f=15n%20%2B%206u%20%3D576%5C%5Cn%20%3D%2051%20-%20u%5C%5C15%2851%20-%20u%29%20%2B%206u%20%3D%20576%5C%5C765-15u%20%2B%206u%20%3D%20576%5C%5Ccollect%20like%20terms%5C%5C765-576%3D15u%20-%206u%5C%5C189%3D9u%5C%5C9u%2F9%20%3D%20189%2F9%5C%5Cu%20%3D%2021)
Let's put the value of u into equation (i)
![n + u = 51\\u = 21\\n + 21 = 51\\n = 51 - 21\\n = 30](https://tex.z-dn.net/?f=n%20%2B%20u%20%3D%2051%5C%5Cu%20%3D%2021%5C%5Cn%20%2B%2021%20%3D%2051%5C%5Cn%20%3D%2051%20-%2021%5C%5Cn%20%3D%2030)
From the calculations above, the numbers of new CDs is 30 and the old CDs is 21.
Learn more on system of equations here;
brainly.com/question/13729904
Answer:
Breadth = 8 cm
Length = 17 cm
Step-by-step explanation:
Given rectangle:
Breadth = x cm
Length = x + 9 cm
Area = length * breadth
= x * (x + 9)
= x² + 9x
Rectangle with length and breadth increased:
Breadth = x + 3 cm
Length = x + 9 + 3 = x + 12 cm
Area = 84 + (x² + 9x) cm²
(x +3) * (x +12) = 84 + x² + 9x
Use FOIL method
x*x + x*12 + 3*x + 3*12 = 84 + x² + 9x
x² + 12x + 3x + 36 = 84 + x² + 9x {add the like terms}
x² + 15x + 36 = 84 + x² + 9x
x² + 15x + 36 - 84 - x² - 9x = 0
6x - 48 = 0
6x = 48
x = 48/6
x = 8
Breadth = x = 8 cm
Length = x + 9 = 8 +9 = 17 cm
Answer:
14 blocks
Step-by-step explanation: