Answer:
99 marbles
Step-by-step explanation:
Let number of marbles with Alex be ![x](https://tex.z-dn.net/?f=x)
Leanne has 1/2 as many marbles as Alex.
So,
Number of marbles with Leanne = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
Number of marbles with Joachim = ![\frac{2}{3}(\frac{x}{2})=\frac{x}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%28%5Cfrac%7Bx%7D%7B2%7D%29%3D%5Cfrac%7Bx%7D%7B3%7D)
Also, Alex has 36 more marbles than Joachim.
So,
Number of marbles with Alex = 36 + Number of marbles with Joachim
= ![36+\frac{x}{3}](https://tex.z-dn.net/?f=36%2B%5Cfrac%7Bx%7D%7B3%7D)
So,
![x=36+\frac{x}{3}\\\\x-\frac{x}{3}=36\\\\\frac{2x}{3}=36\\\\\x=36(\frac{3}{2})\\\\x=54](https://tex.z-dn.net/?f=x%3D36%2B%5Cfrac%7Bx%7D%7B3%7D%5C%5C%5C%5Cx-%5Cfrac%7Bx%7D%7B3%7D%3D36%5C%5C%5C%5C%5Cfrac%7B2x%7D%7B3%7D%3D36%5C%5C%5C%5C%5Cx%3D36%28%5Cfrac%7B3%7D%7B2%7D%29%5C%5C%5C%5Cx%3D54)
So,
Number of marbles with Alex = 54
Number of marbles with Leanne = ![\frac{x}{2}=\frac{54}{2}=27](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%3D%5Cfrac%7B54%7D%7B2%7D%3D27)
Number of marbles with Joachim = ![\frac{x}{3}=\frac{54}{3}=18](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3%7D%3D%5Cfrac%7B54%7D%7B3%7D%3D18)
Total number of marbles = ![54+27+18=99](https://tex.z-dn.net/?f=54%2B27%2B18%3D99)
Answer:
189.3 unit^2.
Step-by-step explanation:
The total area = area of the rectangle + the area of the semicircle
= 15*10 + 0.5 π*5^2 ( note the radius = 5)
= 150 + 12.5 π
= 150 + 39.3
= 189.3 unit^2.