Respuesta :
Using a system of equations, the amounts of gems collected by each member is are given as follows:
- Cecil: 13
- Alice: 40
- Jaime: 108
- Amir: 3
- Monte: 18.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
- Variable x: Number of gems collected by Cecil.
- Variable y: Number of gems collected by Alice.
- Variable z: Number of gems collected by Jaime.
- Variable t: Number of gems collected by Amir.
- Variable w: Number of gems collected by Monte.
They collected a total of 182 gems, hence:
x + y + z + t + w = 182.
Alice collected 1 more than 3 times what Cecil did, hence:
y = 3x + 1.
Jaime collected 12 less than 3 times what Alice did, hence:
z = 3y - 12 = 3(3x + 1) - 12 = 9x - 9.
Amir collected 10 less than Cecil, hence:
t = x - 10.
Monte collected 5 more than Cecil, hence:
w = x + 5.
Replacing everything in the first equation, we can solve for x as follows:
x + y + z + t + w = 182.
x + 3x + 1 + 9x - 9 + x - 10 + x + 5 = 182.
15x = 195
x = 195/15
x = 13.
Hence the other variables are:
- y = 3(13) + 1 = 40.
- z = 9x - 9 = 9(13) - 9 = 108.
- t = x - 10 = 13 - 10 = 3.
- w = x + 5 = 13 + 5 = 18.
Thus the amounts of gems collected by each member is are given as follows:
- Cecil: 13
- Alice: 40
- Jaime: 108
- Amir: 3
- Monte: 18.
More can be learned about a system of equations at https://brainly.com/question/24342899
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